Don't.Please, don't.Are you going to automate reading the tanks test status too?Way, way too dangerous.
My old compressor had a pressure switch on it that would turn it off. It was adjustable.You will either need a separate switch for each pressure level or something like a digital gauge with a serial output hooked up the the arduino. ( or just a pressure sensor instead of 3 pressure switches).If you use the 3 pressure switches then just use a 3 way switch to decide on which switch to activate by. A 3 way switch is way easier and cheaper to implement than an Arduino.But if you do use an Arduino you may as well add in a display and have it act as an hour meter too. Go a bit further and chuck a Nitrox/Tx blending stick on it with the O2 sensor feeding the Arduino too.