what will happen when i change insurance and i underwent an operation?

depends on Obamacare and the "pre-existing" or not rules.

Yes, you are charged after the operation. Actually, the bill is sent to your insurance company first, and then the hospitals, doctors, anethesioligists ,,,, bill you later. {I am not kidding. They all send out their own bills - which is why, if we had to have socialized medicine, the one payer system would be the way to go. That would also set prices more uniformly.}

[I would do it in 2013, especially if you have already fulfilled (or would "overfill") your deductible.]

So you had better start calling around, and asking questions, especially since some insurance companies will not have to comply with Obummercare next year due to all of the snafu's.