Popping out of the air cleaner likely means that an intake valve/valve seat are leaking. The combustion in the cylinder leaks past the intake valve, which ignites the air/fuel mix in the intake manifold.
There's other possible causes--none of them good. A failed head gasket could potentially do about the same thing, depending on which cylinders are involved.
Leaking valves and failed head gaskets are best confirmed with a cylinder leakdown test. However, a cranking compression test is sometimes enough.
First Guess: Heads get removed. Head gaskets get replaced. Time for a valve job.
My '88 K1500 did this a few years ago. Head gasket failed between #3 and #5. When the spark ignited #3, a jet of burning gasses blew across the blown gasket into #5. The hot combustion gasses blowtorched a gouge between the two cylinders in the block, and in the head. The block MIGHT be salvageable with significant machine work. The head will go in the recycle bin. The longer you allow the engine to run like this, the worse the damage will be.