When John Travolta strutted onto the “Gotti” set in costume, John Gotti’s spirit was present. Literally. John Gotti Jr. gave the star his dad’s shirts, cufflinks, watches, pocket squares, the whole wardrobe. Get close to his neckties and you could still smell the notorious mobster’s cologne. “His coat fit me,” says Travolta. “His jewelry fit my hands.”

So did the role. The two Johns rose to prominence at the same time. “We were kind of paralleling in our fame. But by the time he rose to his peak, I was already on my third comeback in movies.”

The opening credits sequence of “Gotti” is a documentary montage spliced from paparazzi footage of the mafia boss – the actual one – grinning through herds of photographers as he steps out of fancy cars and strolls down Manhattan sidewalks. It’s a chronicle of celebrity that Travolta himself has lived plenty. As director Kevin Connolly cuts from the real Gotti to him, the faces change but their shared lives are the link.

Gotti was the mafia’s first made man in 15 years, and “the last modern gangster ever,” says Travolta. He wanted to play Gotti as soon as he read Lem Dobbs and Leo Rossi’s script. “Gotti’s” not just about goons betraying goons, though there’s plenty of that. It’s also a neighborhood portrait of the lives that orbit New York City, the dregs, the dreamers, and the guys like Gotti who get things done. The first shot of Travolta’s Gotti finds him looking across the bridge to Manhattan, a violent version of wistful Tony Manero.

Asked if he expects Sammy “The Bull” Gravano, whose testimony sent Gotti to jail, to see the film, Travolta mock-exhales, “Probably! But I don’t know what to say about that!”

Travolta’s Gotti is a fighter, a schemer and a gossip. The actor turns Gotti’s limp — an injury from a construction site robbery gone wrong when the crook was just 14 — into a stiff, get-out-of-my-way swagger. Mobster movies tend to have more plot threads than character development, but Travolta keeps his focus on the man, whom he portrays from 32 to 61.

As a young wannabe under underboss Nell Dellacroce (an imposing Stacy Keach), he’s an ambitious student. In his scenes with Victoria Gotti, played with passion by Kelly Preston, Travolta’s real-life wife of 27-years, he’s a devoted husband. He growls about gentrification, gives grand lectures about crooked dignity, and stays poised, even funny, in courtrooms even when the noose is starting to squeeze.

Growing up as an Italian-American kid in Englewood, N.J., a straight shot across the river from the Gambino family’s turf in the Bronx, Travolta didn’t believe the mob existed. He heard stories, sure — scary stories about people getting killed. But his father, Salvatore, convinced him the mafia was make-believe, “so I wouldn’t worry.”

Now, everyone believes in John Gotti, who charmed, and slew, his way to becoming the media darling Dapper Don. He’s been dead for almost 16 years — after a painful four-year fight with cancer while incarcerated at a federal prison in Missouri — but, as Travolta points out, the Gotti legend is still name-checked in half the hip-hop albums on the shelves. In fact, when Pitbull heard about the film, he called Travolta and asked to do the music. (Travolta said yes.)

Travolta also got obsessed. When director Kevin Connolly first walked into his trailer, the actor had taped photos of Gotti all over the wall. “Scenes and pictures and eras, John Gotti in the ’70s, the ’80s, the ’90s,” Connolly laughs. “It was crazy — it was like a work of art.” Directing him, says Connolly, was “like operating heavy machinery.” Difficult work was effortless because Travolta came prepared. He’d wait two hours after his scenes wrapped just to ask Connolly if they could adjust one of the next day’s lines, and the next morning when he’d arrive, he’d have prepared three different versions of its delivery.

And from the minute he’d show up, the entire set knew it was time to get focused. “He sets the tone,” says Connolly. “All the chit chat stops and we’re there to do the scene.”

“Gotti” was a scrappy, independent shoot — “a grind,” says Connolly. One day, their camera truck broke down on a random suburban street in Cincinnati. It was 98 degrees, and while everyone ran around in a panic, Travolta, still in his Gotti threads, calmly hung out with an elderly couple on their front lawn talking about swimming pools and yard work. “They were just having the most normal conversation,” says Connolly, and when it was time to start filming again, Travolta snapped back into the scene.

Another rough day, Connolly knew he barely had to direct at all. They’d reached the pages where the Gottis mourn the death of their 12-year-old son, Frank, run over by a car in front of their house. Two grieving parents playing two grieving parents in a sequence that’s the bleeding heart of the film. Everyone was aware of what was happening — what needed to happen — and privately decided it didn’t need to be discussed. “Whatever emotions might have been there, they were not on the set,” says Connolly, “they were in the scene. “

The surviving family was also on set. John Gotti Jr., the son who figures largest in the film as he wrestles with his father’s questionable advice to never plead guilty, became close with Travolta over dinners and intense discussions about capturing his father. “He was there every day quality controlling the storytelling,” says Travolta. “Much of the performance was influenced by John Jr.’s truths.”

It was over those meals that Travolta realized “Gotti” had to get a bigger release than he and the other producers had first imagined. When he and John Jr. would leave the restaurant, 300 photographers had clustered outside. “I’ve experienced that at a premiere, let’s say, but going out to dinner? There’s some organic interest they have in my name and his name together — an untapped area that might really surprise people.” For the moment, all Travolta can do now that he’s done the best job he can is look forward to the film’s Cannes premiere — “I felt like we were on our way once we were accepted!” — as “Gotti’s” closing words ring in his ears: “You’re never gonna see another guy like me if you live to be 5000.”