Hi,Sometimes overhead line do come close to each other such that they make contacts(ie they short).Apart form swinging due to wind is it true to say that magnetism due to current in them is one of the effect?

What is the effect of the mesh wire thats always put below the transmission lines at some points?

 

I would not say that the magnetic field created around the transmission lines is strong enough to attract each other. Also, this magnetic field is not always attractive because of the phase shift the currents have in the lines.

With 'mesh wire' you mean the neutral? How many wires are on the pole?

 

Not the neutral but, below the 3 lines running horizontally a 'net' of wires is put about 2-3 feet below the overlines.
To the 2nd que ,there are 3 lives(phases) for transmission but for distribution to consumers they are 4.The 4th being a neutral from the transformer.