Your ECU will always try to keep your Air/Fuel ratio at 14.7 when in a closed loop. Typically anytime below 4500RPM or when traveling up steep inclines the ECU will be in a closed loop.
This causes a hesitation or stumble when travel back and forth between vacuum and boost becuase the ECU wants to see 14.7 while your Auxiliary Fuel Pressure Regulator (AFPR) is dumping in excess fuel at the same time.
An easy (a few wires) and safe (no lean tip-in when entering boost) solution is an o2 clamp. Typically they use a pressure switch that is connected into a vacuum line. When the switch sees a certain amount of boost (usually .5psi), they trigger the o2 clamp to trick the ECU into thinking that no extra fuel is being added. This will ensure that all your added fuel will be there when demanded upon and you will get rid of the stumble.
O2 clamp can be seen installed next to the ECU. (Black box with green LED)
Pressure switch used to trigger the o2 clamp once in boost.
User: Olderguy @ Miataturbo.net