Need help 2001 neon

I have a 2001 neon that every once in
awhile I'll be driving down the road and then
it will start sputtering and back firing until I
hit the gas all the way.  Then it will
accelarate normally until I let off the gas
then it will sputter again. Also when I turn
on the heater in the morning it idles normal
then high then normal and high until the
heater is off.  Thanks.  Recenetly replaced
wires plugs cattylitic converter air filter and
downstream 02 sensor.  Both o2 sensor
turn up codes for running rich.