What if?

At 11.30 a.m. (US time), Joe Biden takes the oath of office as vice-president. So at least Cheney's out of the way, but Bush is still President. So if Bush has a heart-attack (out of sheer Texan fury) before Obama is sworn in, does Biden become President? Does Biden have any authority as VP while Bush is still President or is it only activated when Obama's sworn-in at 12.00? What if Obama has a heart-attack (or gets shot) between Biden's oath and his own? Who's in charge?