Step 2: Hacking
So the switch to go UP and DOWN is like a pair of switches to light up a lamp each one, that is why we need 4 relays, and we will control with an arduino to switch every pair to move the motor in every direction.
You can see the diagram bellow [photo #2], also how it looks like in our motor. We had problems managing the direction, but Eric Rosenthal gave us an explanation and a solution for the problem. When we control AC motors with the solid state relays, the relays don't discharge the capacitor but the switch does it someway. So when the capacitor is not being discharged, the motor will go on the same direction as the charge. The solution is the inclusion of a resistor (200KΩ) between both terminals of the capacitor which will discharge the capacitor when the motor is not operating (we didn't have 200KΩ resistor, so we used two 100KΩ connected in series).
After having done this we hacked also another motor, but this one had two capacitors connected in parallel so I connected 200KΩ in every capacitor (I am not completely sure about this, but it works at least) [photo #8].