The trickle of Cuban baseball players filtering into the majors has grown into a torrent, with their numbers increasing to an all-time high of 30 last season.

Yet despite their rising levels of success and skyrocketing salaries, Cuban players across generations share the heartache of leaving behind their country, family and way of life, experiencing a longing for their homeland that simmers down but never quite gets extinguished with the passage of time.

That’s one of the central themes of Cuba: Island of Baseball, an MLB Network documentary that debuts Tuesday night.

Released nearly two years to the day when President Obama and Cuban president Raul Castro announced a normalizing of relations between the long-estranged nations, the film traces the trajectory of Cuban players in exile.

From the likes of Luis Tiant and Tony Oliva, who joined major league organizations before then-Cuban leader Fidel Castro banned professional sports in 1961, to modern-day defectors like Aroldis Chapman and Jose Abreu, there’s a common bond among players who left the island nation, in many cases never to go back.

“People in this country have an idea of Cuba as being closed and the intrigue and mystery, and they don’t really understand a lot of the back story of what so many of these guys go through,’’ said Danny Field, who combined forces with fellow producers Alfonso Pozzo and Jed Tuminaro.

“So we wanted to tell some of these stories of what it means to be a Cuban player in the big leagues. … The stories repeat themselves, and you see it when Luis Tiant is talking about Yoan Moncada. He relates, and there’s half a century between those guys.’’

Narrated by Cuban American Bobby Cannavale,, the documentary maintains a safe distance from political themes and focuses instead on human stories: Abreu yearning to reunite with his son; Jon Jay searching for his grandparents’ former house; Tiant hesitating to return to the island amid concern about how he will be received; several examples of the difficult transition to a new life in a strange land, where the off-field adjustments have often proved more challenging than the baseball aspect.

Filming began during MLB’s goodwill tour of Cuba in December 2015, which marked the first trip back to their home country for Abreu, Yasiel Puig, Alexei Ramirez and Brayan Pena.

Jay, a seven-year outfielder who signed two weeks ago with the Chicago Cubs, was also part of the traveling party to his ancestral homeland. Born and raised in Miami to Cuban parents, Jay made time in a busy schedule of children’s clinics and appearances to locate his grandparents’ neighborhood in Matanzas, then spent two hours asking around until finding where they used to live.

“Walking around the streets, I feel at home,’’ Jay says in the film. “I feel like this is somewhere where I definitely could have seen myself growing up or living, having that comfort level and that peace in my heart knowing, ‘Wow, this is where my family comes from.’’’

Three months after that trip, MLB returned to Cuba at the same time Obama became the first sitting U.S. president to visit since 1928. The significance of the occasion is captured in scenes at Estadio Latinoamericano, where Obama and Raul Castro sit side-by-side for an exhibition game between the Tampa Bay Rays and the Cuban national team.

Tiant, having overcome his reservations to return to his native land for just the second time since 1961, gets complimented by Obama as he stops by and shakes hands with both leaders. Later in the documentary, Tiant comments on being in the awkward position of exchanging greetings with one of the men responsible for his exile and that of hundreds of thousands of his countrymen.

“What are you going to do?’’ the four-time 20-game winner says. “Are you going to take your hand away from him? Are you going to turn your back on him? Everybody in the world would see that. To me, that’s a disrespect. No matter if you like him or not, he’s the president of the country. You don’t want to do that to any president, I don’t care what you are.’’

Cuba: Island of Baseball also pays tribute to the trailblazing players who initially left everything behind to try their fortunes in the major leagues, among them Barbaro Garbey and Rene Arocha.

Garbey, who had been suspended for game-fixing in Cuba, arrived in the U.S. through the Mariel boatlift in 1980. He signed with the Detroit Tigers and played three years in the majors, including the 1984 World Series-winning season.

Arocha was the first member of the Cuban national team to defect, staying in Miami during a layover in 1991 and seeking asylum. His career in the majors lasted just three-plus seasons, but Arocha is credited with opening the door for the wave of talent to follow, even though Garbey preceded him.

“The most fascinating story for me was Barbaro Garbey,’’ said senior producer Pozzo, a Cuban American who grew up in Honduras. “I didn’t know his story. I thought Arocha was the first one, and here I am a baseball guy.

“I wasn’t sure if he would talk about (the suspension) when I was doing the interview with him. I wasn’t sure how I was going to approach it when I sat down with him, and he was very open about it from the beginning.’’

Coming from a Communist regime that fostered paranoia among its citizens, Cuban players are typically tightlipped about their defections. Only one of the subjects in the documentary – catcher Brayan Pena, most recently with the St. Louis Cardinals – offers details about how he escaped.

But the producers have a history interacting with the Cuban baseball federation and its players, several of whom they have covered in the World Baseball Classic. That facilitated access to Antonio Castro, the federation vice president who is quoted extensively, and helped elicit heartfelt narratives from the players.

“I’m maybe more the American target audience where a lot of these players to me existed in scouting reports,’’ said Tuminaro, the coordinating producer. “What can they do for my team while they’re here? And when the season’s over, you’re done. You don’t think about them not being able to go home and see people. The one story where Abreu is on the plane looking out the window waiting to see his son, that stuff really hit me hard.

“The situations may be all be different for every person, but one underlying thing they all deal with is this almost emotional tug-of-war between the decision to come and play baseball and what they leave behind.’’

Cuban players on both sides of the Florida straits yearn for the day when they can come and go freely between their native country and the U.S. Two major events that took place after the document’s filming was concluded could have an impact on the likelihood of that happening, although it’s not clear to what extent.

One was the presidential election of Donald Trump, who has sent mixed signals regarding his opinion of Obama’s policy change toward Cuba. The other one is Fidel Castro’s death on Nov. 25.

Pena, who has been a U.S. citizen for several years but retains close ties to the island, is among those watching closely.

“I’m hopeful the government of President Trump realizes my people need help,’’ Pena told USA TODAY Sports. “The people of Cuba are suffering, and I hope President Trump does what’s needed to improve the Cuban people’s democracy. But we don’t know how he’ll act, so we have to wait and see what’s coming.’’

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