While I’m not a big fan of the Grateful Dead, I’m eternally grateful to Jerry Garcia for saving “The Saragossa Manuscript.” Back in the 1960s when rock music, movies, drugs, and politics were one big, simmering witch’s brew, the Polish director Wojciech Has’s “The Saragossa Manuscript” screened at the San Francisco Film Festival.

Garcia saw it, fell in love, and bought a print which he gave to the Pacific Film Archive on the condition that they would screen it for him whenever he asked. Martin Scorsese and Francis Ford Coppola also fell under the film’s spell, and eventually they all raised money to have the print restored. The resulting three-hour “Saragossa Manuscript” will screening at the Brooklyn Academy of Music for the next week, and even a cynic will quickly see how it can seduce the unwary.

Jan Potocki was an early hot air balloonist who wrote “The Manuscript Found in Saragossa” in 1814. The book related the nomadic tales of a nobleman during a 66-day mule trip through the mountains of 18th-century Spain. More than a century and a half later, Wojciech turned it into a film, and it’s one of the only movies entirely powered by hot air.

“Saragossa” kicks off during the Napoleonic Wars, when a French officer finds “The Saragossa Manuscript” as his army sacks the Spanish city of Saragossa. He begins to read it as bombs fall outside, and is soon caught up in the tale of Alphonse van Worden (Zbigniew Cybulski, known as the Polish James Dean), a Belgian captain in the Walloon Guards who is traveling through a blasted countryside trying to reach Madrid.

In the story, Alphonse takes refuge in a house that may or may not conceal a secret cabal of Islamic princesses in the basement. He may be drugged; he is definitely captured by what may or may not be the Spanish Inquisition, and he definitely cannot escape the abandoned house. Beyond that, everything is up for grabs, or rather “gabs,” because every character he encounters has a story to tell — and the characters in their stories tell stories, which also feature characters telling stories.

By the time we’re watching a story being related to us by another character in a story that was being told to us by a character in yet another story, who is part of a story being told to us by yet another character in the very first story, who was, after all, a character in a book being read in the bombed-out ruins of Saragossa, the feeling is akin to drowning in a ball of yarns.

But rather than coming off as a remote, overly intellectual exercise in audience bafflement, “The Saragossa Manuscript” is vitally alive — full of lovers, duelists, topless nuns, cowards, and magicians. Its veins run hot with black-and-white blood, and whenever a scene begins to drag, someone inevitably interrupts with, “This reminds me of a story…”

As the film proceeds, the stories pick up speed like a runaway train and baby-faced Alphonse does his best to keep up. Initially he’s terrified that these occult stories pose a threat to his immortal soul, but soon he’s wrapped in their narratives, desperate to know what happens next. In real life, Cybulski met a similar fate as Dean when he fell beneath a railway car and was killed at age 39. But in “Saragossa,” it turns out that all the threats are shams; the Devil won’t get you no matter how many stories you hear, and Potocki reserves for his character a triumphant ride into the sunset that he never afforded himself.

Through April 10 (30 Lafayette Ave., between Ashland Place and St. Felix Street, Brooklyn, 718-636-4100).