My 02 cavalier will not shift when I quickly press accelerator it just revs up but if I let off gas and I ease into it like normal it shifts smooth. Just changed transmission fluid and filter along with throttle position sensor and cleaned the idle air control valve. It doesn't seem like the transmission itself is going bad because it shifts to good with normal driving. Was wondering about the passing gear. If it has a sensor or maybe a shift sensor.

I would be looking for vacuum hose leaks to the vacuum actuator on the transmission
what you describe indicates either no vacuum or a faulty actuator that causes a shift in gears in the transmission not to be effected
run the fault codes to see if any other sensor ot TCM is involved in the problem
this is all indicated by the changes that occur when you ease of the accelerator and it changes gears

Assuming you have an auto transmission, your only choice is to ease off the gas when you want it to change gears. Then apply slight pressure on the gas to continue to accelerate.

The transmission has servo shift sensor and can be affected by the speed sensor . Should the speed sensor not be the problem and it the other I recommend you find a used transmission with low mileage seek an experience mechanic to install with new fluids in tranny and torque convertor

you need to let the RPMs drop down to match the speed you're going for the next gear, though this is less efficient than power shifting through.
Unless you're slipping the clutch to smooth out the gear change, yes, there will be a definite surge every time you grab a gear in a manual transmission vehicle. Most automatics will also shift noticeably harder at WOT.
For more sedate, "normal" driving, you can shift slower and feather the throttle a bit more to smooth out the gear changes, but when you're ******* the throttle as soon as the clutch engages, it's going to be a firm shift. I hope is ok.

i have the same issue with my 92 lx. when i press on the gas n ease off the clutch its not getting power at all. almost to 35mph when in third gear and thats not withough shifting to early too. lemme know if you get urs good please.

would be worth having the cat converter check for blocking the exhaust system

when vw started to use the computer controlled gearbox system a criticism was the shift was very harsh,to counter this they made it rev slightly before changing.so that you know the system, try this out....without touching the gas.....put it in d and let the car accelerate to its max speed,stop,then use 1/3rd of gas (keep your foot still)and let it do the same...stop,then,if safe,put your foot to the floor,hard, notice when the car changes gear(revs/speed)then if you drive,only using the first1/3rd of the gas,the cars change pattern will alter to suit.......wierd it is.....

Check the catalytic converter. You can do this by banging on it and listen for a rattle. Sometimes, the inside gets melted into a little ball and blocks the exhaust from getting out on acceleration. This will cause a serious loss of power and feel like a trans malfunction.

Your lockup torque converter is bad I believe. When you shift from Park into any gear it will die.

sounds like it may be either a converter problem or u got some bad clutches in third in the case you need to go to a tranny shop.