first lets resolve the positioning of the MAF before asking bout the BOV.
any air flowing through the airflow meter will be detected by the ECU and more airflow = more fuel.
If the BOV vents to atmosphere and the active mass airflow meter is ahead of the BOV, whenever the throttle is closed during boost, the turbo is still winding down so air is still flowing through the filter, turbo, airflow meter and then out the BOV. all that excess air flowing through the MAF is still registered by the ECU (even though it hasn't entered the engine) and so it injects the amount of fuel relative to what it senses resulting in a brief rich mixture until the throttle position sensor see's the throttle is fully closed whilst the rpm is above 1k and cuts fuel.
If the BOV recirculates back into the turbo inlet but the active airflow meter is still located within the recirculation pathway (between the BOV and where the recirculation pipe enters the turbo inlet), when the throttle is closed during boost, air is still flowing through the fast spinning turbo, out the BOV, recirculated back into the turbo inlet and through the MAF, and the ecu once again assumes all that fast flowing air must be entering the engine and injects too much fuel.
If the BOV recirculates back into the turbo inlet, the BOV should be located away from the "recirculation pathway" (either between the filter and where the recirculation pipe enters the turbo inlet, or between the BOV and inlet manifold) so when the throttle is shut, the recirculated air is whizzing very quickly between the BOV and turbo inlet but the MAF located away from the "recirculation pathway" only detects the total amount of air actually entering the engine.
best location for the active airflow meter is between the BOV and inlet manifold (whether it's the stock TB MAF or an external MAF) cos it'll register whats actually entering the engine irregardless of what the turbo plumbings doing ahead.
vent to atmosphere vs recirculation?
imo vent to atmosphere is more for showing off and can cause MAF issues as explained above and actually allows the turbo to wind down faster during closed throttle cos the turbo has sacrificed all of its available spinning energy to compress all that precious energised air which is simply wasted away so the next time the throttle is open (ie during up-shift), the turbo has to slowly spin back up to speed before producing enough boost, therefore feels laggy
a recirculation system recycles all that pressurised air back into the turbo system even though the engine doesn't need it, so the excess pressure is fed back into the turbo impeller to keep it spinning for longer. this means the turbo winds down alot slower during closed throttle so the next time the throttle opens during up-shift, the turbo is more up-to speed and responds faster compared to a vent-to-atmomosphere system.
the recycled boost energy also results in quieter operation whereas a vent-to-atmosphere BOV simply expels that energy out as sound energy
where is your MAF ?
