Almost inevitably, critics bring up the Beatles when they write about their ill-fated American successors of the ‘70s, Big Star. However, had those gifted Memphians been nothing more than slavish Fab Four imitators, I wouldn’t be writing about them today.

Certainly, Big Star’s original principals Chris Bell and Alex Chilton absorbed the melodic and harmonic influence of the Liverpool quartet. And, like their hit-making English models, the American Southerners were fortunate enough to have nearly unlimited access to a recording studio – in their case, Ardent, the state-of-the-art facility that was also home to the like-named indie label that issued their music.

But Bell and Chilton’s music was in the end something utterly different and original. Reflecting their geographical birthplace, many – most – of Big Star’s songs move at humid half-speed, as if mired in Mississippi riverbank mud. There’s a melancholy undertow to their sound, a tug at the bottom you don’t hear in other contemporary pop. It’s the minor chords in their songs that you recall most vividly.

The titles of their first two albums, #1 Record (1972) and Radio City (1974), were full of hope. But Big Star failed to take the commercial high ground, thanks to the financial disarray of Ardent’s first distributor, Stax Records, and the indifference of its second, CBS. By the time Chilton and drummer Jody Stephens entered the studio for the sessions that became the deranged, belatedly released Third/Sister Lovers (1978), the group was forgotten by all but a few.

They’ve since had their day in the court of critical opinion, though, and their apotheosis came in 2009. Fantasy Records brought forth an improved two-fer edition of Big Star’s first two albums. Now Rhino Records has stepped up with Keep An Eye On the Sky, a jazzy four-CD box bursting with unreleased goodness.

The box does not supersede the official versions of the first two albums, though it presents Third basically as it was released. Instead, its first two discs reconsider #1 Record and Radio City through a bounty of variants – alternate takes, alternate mixes, single versions. Some of the stuff has seen prior release – on the 2008 English anthology Thank You Friends: The Ardent Records Story and a 2003 collection of Bell’s pre-Big Star work with the bands Icewater and Rock City.

But there’s enough that’s rare and previously unheard here to divert the most Star-struck of listeners. Over and above some tremendous demos (which include Big Star’s versions of tracks later unearthed on Bell’s album) and revealing, crystalline-sounding alternates, there’s a CD of hitherto unreleased live material. Drawn from shows at Lafayette’s Music Room in Memphis, in which the Radio City-era trio of Chilton, Stephens, and bassist Andy Hummel tried to entertain a disinterested crowd waiting for Archie Bell and the Drells, this stuff offers a rare glimpse of the group’s solid live chops.

Long one of rock’s great woulda-shoulda-coulda-beens, Big Star finally receive supreme respect with Keep An Eye On the Sky. Whether you’re an enthusiastic newcomer to their music or a knowledgeable post-grad fan, you’ll find plenty to embrace and enjoy in this lovingly produced collection. And yes, it’s an ideal complement to those Beatles remasters.