3-phase pump, run on single phase supply??

Wow guys, a little motor knowledge needed here.

Speaking to the original post, Lazza;  what you observed is called a PSC (Permanently Split Capacitor) motor.
It is considered to be a single phase motor since it runs on single phase.
These are called three wire pumps to separate them from two wire pumps that work differently.
This is not three phase.
They have a main winding connected across the line and a second winding that is smaller running at 30 to 50% the current.
The second, smaller winding has a capacitor in series and they are connected across the same line.
The smaller motor winding is wound 90 degrees from the main winding.
The capacitor shifts the phase of the current going to the smaller winding 90 degrees.
Ninety degrees leading is the only phase shift a capacitor can produce.
These motors, even though called single phase, actually are two phase motors with the motor windings separated 90 degrees.
The capacitor stays in the circuit all the time.
A run type capacitor is necessary.
Run capacitors are usually oil filled and are smaller capacity wise (and physically bigger) from a start capacitor.
PSC motors have low starting torque but run higher efficiency.
They have been taking over the field for the last thirty years.
Practically all refrigeration and most fan motors are now PSC.

For reference consider the Capacitor Motor:
The capacitor motor is the same basic 90 degree two phase motor
but has a switch that disconnects the second, smaller winding with capacitor once the motor gets up to speed.
A so called "start" capacitor is used.
The start capacitor is used only for a fraction of a second upon start up.
An bipolar electrolytic capacitor with more capacity can be used which gives the motor much higher starting torque.
A start capacitor works good for the capacitor motor but will burn up when used as a run capacitor for a PSC motor.

Three phase motors have three windings spaced 120 degrees.
Power flow into a three phase motor is steady.
Power flow into a single phase motor goes from 0 to two times average 120 times a second (60 cycle).
This puts more stress on the motor and windings.
Three phase is significantly more efficient.
Three phase motors use less iron and coper for the same Hp, every thing else being the same.

We are starting to see dedicated purpose 90 degree two phase VFDs come into the market.
They are very expensive.
Low cost, general purpose two phase VFDs are not here yet.