I can only speak for the usage of "
rev(ving) the gears" in the car/motorbike milieu I'm familiar with (both in Europe and across the pond).
There's no point in counting Google hits (
Rev engine vs
rev gears) because it's truly apples and oranges
- Rev the gears means to accelerate close to the red line before upshifting. Period.
- Rev the engine could mean the same but it's also widely used to describe a quick
gas input/throttle blip respectively in a car with manual transmission (double-clutching or even double-declutching) or a motorbike while downshifting.
Stretching the gears/Pushing the gears may also work, but I'm unfamiliar with such expressions, which also lend themselves to different interpretations (modifying the gear ratio, reassembling a transmission, etc.)
So where's this leave us?
Other than a highly interesting thread full of passionate contributions, I think we'll all go back to calling those
actions the way we've always called them (and I suspect some contributors still aren't entirely clear on what's what, but hey, it's the Internet

).