Backfire through the intake

It has an intermittent problem. It will start to backfire through the intake and sputter when giving it gas. You have to pump and floor the accelerator to get it going. It slowly picks up speed.
It comes and goes though. It will clear up and run great for awhile then start acting up like this again.

I have done a complete tune up, plugs, wires, distributor cap, rotor, air filter, etc, also changed the wiring to the fuel injectors. None of this helped.
The check engine light does not come on but it is working. The 02 sensor was disconnected to see if the light comes on which it does. It did not throw any codes either according to one mechanic who changed the wiring to the fuel injector.

Do you have any idea what is causing this?