Thank you for your reply!
I went further with my observations, and traced which wires are connected to which hall-effect sensor. I traced the 6 wires to the 3 sensors.
Now what I don't know is if there is polarity in those sensors?
I assume that I have to count this way - 6 output lines from the sensors, power, ground for them, 3 control lines for the coils. (I traced those also). Is that right?
My motor comes from disassembled CD ROM. In it you can find two more motors the one opening the tray, and the one moving the optical head.
I managed to work with the DC motor that positions the head laser reader. On both drives I found a motor with linear optical encoder attached directly to the shaft. Because the encoder is linear (3 wires) and optical (led) I figured out the power and the ground (from the placement of a resistor) and was able to read the ticks from the data pin. (Sorry for the little off topic but I think googlers might find it handy)