Surging RPMs

Ok here is the first of many problems with my car, a 97 eclipse gst. When driving once i am at around 40 mph and let of the gas to idle (yes its auto) the RPMs drop sharply to 1k then pop back up again in the new gear. This happens mostly around 40 mph but has happend at lower speeds occasionally. Also when accelerating when it upshifts from 1st to second the RPMS shoot up to about 4-5k but I dont get any speed. The RPMS just raise up and drop down when the gears shift. This happens at about 25ish and 40MPHs...please help!! Is it a computer chip problem in with the tranny? Is it the turbo leaking? Is it the whole tranny? Ahhh!!