I think it largely depends on how much you associate any individual member with a band and it is largely a personal opinion. Some bands are dominated by individual personalities, some are dominated by the idea of the band itself. For instance, Led Zeppelin is considering releasing a new album without Robert Plant as the lead singer (or John Bonham on drums obviously). To me, Plant is a big enough part of Zeppelin whereas if they released a record without him on lead vocals, I'd have a tough time calling it a Zeppelin record even though Jimmy Page, John Paul Jones, and Jason Bonham were all present (Page especially). The flip side of this is two of my favorite bands - Wilco and Spiritualized - have had tremendous lineup turnover. However, Jeff Tweedy and Jason Pierce respectively are the center of their bands and all parts around them can and have changed, and the band is still essentially the same due to its core member. On the other hand, there are many bands that have undergone wholesale changes to its core and have still continued under the same name to the satisfaction of their fans. Lynyrd Skynyrd comes to mind first for me, Yes, The Jazz Messengers (of course not ignoring that Art Blakey was the constant member), The Yardbirds, maybe Big Star, etc. If you think Axl Rose has always been the driving influence behind GnR so that essentially GnR=Axl Rose, then maybe you could consider it the same band. Music is great that many people can have many differing outlooks on it, so maybe there isn't a definitive answer the question. It's personal taste and affiliation. To me it would be when the essence of the band changes, even to the extent that the same group of musicians starts making drastically different music. For instance when Wire went all new wave in the late 80's-early 90's, I consider it to be a new incarnation of the band and it to be essentially different from the Wire of the late 70's that put out those great albums. Or the Kinks of the same time period. Mercury Rev after Boces was not really the same band at all, though I like them a lot more without Dave Baker. Basically... it's up to the listener to decide.