Bruce Springsteen’s voice sets the tone for Alex Gibney’s riveting documentary portrait of Frank Sinatra: All or Nothing at All. “The Boss” says, I first heard him when my mom and I used to hunt down my dad in New Jersey saloons. Hear that? His mother would say. That’s Frank Sinatra. Even Stevie van Zandt, who attended the premiere at the Time Warner Center this week, raised an eyebrow at Springsteen’s candor. “All or Nothing at All,” the title of one of his songs aptly defines his code; the film neatly weaves Sinatra’s line, a leitmotif, as he rises in artistry and fame, and personally in cycles of sad and sublime. With testimony from Frank’s family, “Italian” wife Nancy, son Frank, Jr., daughters Nancy and Tina, and stunning actress Ava Gardner (her words from a transcribed interview read by Gina Gershon) for whom he left Nancy, the documentary to air this weekend on HBO reveals filmmaker Alex Gibney’s gift for making films that feel like the subjects, even deceased ones, thrive in the next room, still singing and living their successes and troubles.