It\'s not so much running rich at the point you lift off the gas.
Take the time it takes to change gear:
1) Release throttle
2) Change Gear
3) Back on throttle.
The rich condition happens as you get back on throttle.
In a recirculated system where the air is put back post MAF, the ECU has already calculated x liters of air in the system. When you dump it to atmosphere, instead of x-litres, there actually is only x-(volume dumped) liters.
So, when you get back on power (on step (3)), ECU thinks there is x litres, starts squirting fuel to burn x litres, hence rich condition, excess fuel goes out exhaust, back fire, stutter.