OK, here's my .02$$ as far experience from car stuff is concerned with clarifying backfiring and raspberries out of the exhaust. I have owned cars that would throw fireballs out of the back in between shifts and sounded like a .45 when slowing in gear. All normal.
Backfire: this is when combustion comes physically out of the chamber and into and through the intake. Due mostly to mistiming, the event goes past the intake valves and into the airbox. This is way louder than decel popping and way more damaging. The intake valves were not designed to take this abuse because the heat can't be transferred from the face into the seat. That and they're built less robustly because they use fuel as well to cool them on the backside. In extreme cases, you can blow the carbs out of the boots or even the airbox. There are youtube videos of Mustangs that had a nitrous backfire blow apart a cast aluminum manifold on the dyno.
This is bad and something is wrong, no amount of dicking with your carb will fix this. Basically means something is out of time (physical timing or otherwise) and is only a matter of time till something lets go. Ever wonder why that screen exists in your airbox? Yep, it's a backfire screen to help keep your air filter from catching fire if this were to happen.
Raspberries; also know as decel popping: happens naturally under deceleration with closed or partially closed throttle, made even more obvious by an aftermarket can with a straight through baffle. The chambers of a stock muffler help hide this anomaly to an extent. Due to the mixture being sucked into the header pipes between cycles, the mixture then ignites in the pipes (naturally, because they're hot) and voila, popopopop. You can also get this on higher rev shifts between shifts as the mixture is moving so fast in and out of the motor that the interruption will mimic what happens in decel.
Made worse by bikes with PAIR valves that inject air into the exhaust to burn the excess fuel. This is actually not a bad thing and really a byproduct of the cam timing manufacturers use so that the overlap pulls in additional intake and excess exhaust in and out of the chambers.
I have no idea why this is always something that people try to tune out with fuel screws because in theory, it stands to add more fuel to the chamber to possibly make it worse. Ever watch a race when the guys are using maintainance throttle through a corner and you see flame and hear the popopop? That's what that is, a little decel popping on the overrun.
Here's the thing if you try to lean this out: you will raise combustion temperatures and perhaps even start to ping. Ideally, you should make sure the mixture is correct for the amount of air going in and out of the motor and not try to fight the byproduct of this, popping or otherwise, with messing with screws, etc.
Set up your bike so it runs well. If you don't like the popping etc that comes with higher performance stuff that was designed not to suppress this: go back to stock. You cannot tune around some of this stuff, it will only make matters worse.
