It does not reverse any spin. The thing it does is it does not change the spin. What you consider a backspin is a ball spinning towards the opponent if the ball was the same spin was going towards the opponent he would consider it topspin. Same thing if a ball is spinning towards you you consider it topspin if the same ball with the same spin was going towards an opponent he would consider it backspin. So the antispin only changes the direction ball is going without changing spin that much.
Here is the animation with Ling Pimples, the anti-spin has a very similar idea:
It depends on what type of anti. The modern frictionless antis will “reverse” the spin a lot whereas old school antis like Super-Anti and Anti Power will likely send back no spin.