Haven't stayed there my self but I know they are different one from the other.
Lithies is in Firostefani, on the cliff overlooking the caldera.
Merovigla is in Imerovigli and has no caldera view (which is only a few staps away) but has a swimming pool.
Rapsody is at the beggining of Imerovigli, and has view to the East.
So, if you definitely wish to have a swimming pool just choose Merovigla or if view is important choose Lithies. As for Rapsody I bet it is the least expensive one so....
By the way if word of mouth helps I've met people who stayed in Merovigla & Lithies & had no complaints. I haven't met (yet!) anyone from Rapsody so I couldn't say anything.
Have fun whatever you decide!