You need to understand what the neutral wire really is. At the pole there's a transformer that converts (steps down) a very high voltage to the residential 240 volts, AC. On the residential side you'll see 3 wires going to the house and into the breaker box. 2 wires are the ends of the transformer secondary coil at the street and the other is the center tap of that coil. The voltage between either transformer end wire and the center tap is 120 volts. The center tap is always zero volts and is the neutral. Since the phase of the voltage is 180 degrees out of phase, between the end wires of the transformer you get 240 volts.
You can hold the neutral and have no worries because it's the center tap of the transformer and usually bonded to the earth ground at the breaker box. However to have a complete circuit you'll need to have the return current flow through the neutral to the center tap of the power transformer secondary.
A capacitor in a psc motor is used to alter the phase of the electric current so there's a torque on the motor armature causing it to spin. Now if it's a 240 volt motor, the neutral is not needed and they will us the 2 transformer end wires, L1 and L2. If it's a 120 volt motor then you'll use L1 and the neutral.