It is illegal to carry on your person or in a carry-on bag any container of pepper spray. It is not, on the other hand, illegal to put a pepper spray container in another bag that will be stowed underneath on an airplane. Because of this, if you are intending on bringing your own pepper spray out of America and to another country it's important to pack your pepper spray separately. You should also put it in some kind of holster so that it doesn't accidentally discharge during transit.
Pepper spray, by Italian law, is considered to be a legal, defensive weapon. This means that you can bring your own pepper spray for self defense, or you can purchase pepper spray once you arrive in Italy. Pepper spray is made from the plants of the capsicum genus, including chile peppers. It irritates the skin and causes a reaction in the body that swells the eyes closed, makes breathing hard and makes the nose run. This sort of spray is called OC spray, and by Italian law it's legal as long as it has only a 10 percent OC concentration.
It's extremely important when you're carrying pepper spray that you use it only when you feel that you're being threatened. If you use your pepper spray on someone and you were not protecting yourself, then you have just committed criminal assault with a less-than-lethal weapon. Circumstances not in your favor would be if you were intoxicated, you started a fight or you kept using the pepper spray even once the other person backed off. It's very important that you be sure you're in danger before defending yourself this way.