How to synchronize three power sources, one of a battery bank 120v output Inverter pure sine wave, and two more single phase 120v at my house, to obtain three-phase for an electric motor
Many hybrid inverters allow three inverters to run in freq sync but each with 120 degrees phase shift between units to create three phase output.
A three phase motor can often be run from single phase source with a run capacitor in series in one of other phase connections on motor. You can Google the details of what to do for given motor size. Motor needs to be wired in delta configuration or access to center neutral connection for a wye configuration. Rotation direction will depend on which of other two windings you put cap it series with. You won't get full HP rating on motor, but it is a lot cheaper to do if you don't need full motor power.
Panto, the vectors of the two phases in your home are 180deg apart, whereas 3-phase power vectors are 120deg apart. Check out DPS Store on Amazon (Digital Phase Shifter) for more info.