The Beggs-Muller ‘Emergency Spin Recovery’ method which Gene Beggs wrote specifically for the Pitts Specials is…
Throttle to Idle, Let Go of the Stick, Apply Full Opposite Rudder to the direction of yaw - as determined by sighting down the top of the engine cowling at the ground.
Gene says that after thousands of spins that this method will stop any spin in the Pitts whether upright or inverted, flat or accelerated.
It is noticeable if you look at the stick while doing this that initially the controls trail in the relative wind, eg if the spin was upright the stick will remain rear of neutral. This is where you want it in the Pitts which suffers from the tail plane and elevator considerably preventing the rudder from getting good airflow over it in an upright spin. This is made worse if the stick is pushed forward prematurely.
Similarly, hands off, the stick is deflected slightly into the roll component of the spin. Again this is where you want it in the Pitts because it gives that wing less drag (aileron up). Perhaps more importantly it gives the other wing more drag.
When the anti-spin rudder (the Primary) and the little bit of in-spin aileron take effect and the rotation slows almost to a stop, the natural stability of the aeroplane takes over.
The stick snaps into the central position by itself and after centralising the rudder you can recover to normal flight. Again, this is what Pitts biplanes will do. Other types may not, indeed some will not.
Therefore, as many others have said, you should follow the flight manual procedure for the aircraft type.
Even more importantly, get dual instruction for spins as they can be disorienting. A neophyte may let the anti-spin rudder come off the stop or even have no idea which way the aircraft is spinning.
Control friction may prevent the ailerons going where they should and in types with considerable ‘washout’ (wing twist) on (for example) high-wing Cessnas an outboard wing may remain un-stalled in a spin. In-spin aileron would be counterproductive in that case.