Examples:
a1) Vivo a Roma.
It means: and my activities are in Rome and (probably) my house is in Rome.
a2) Abito a Monza ma vivo a MIlano
I have my house in 'Monza', but I live in Milan.
Here 'vivere' means: (almost) all my activities, my interests, my friends are in Milan.
Note: Monza is very near to Milan.
'Abitare' is mostly related to where the house is.
'Vivere' is mostly related where the activities are.
Usually the two places are just the same, so we usually add to abitare the meaning of vivere
and viceversa.
/vivere/ in the form NOT related to /abitare/ means:
1. to be alive
2. to spend one's lifetime
v1) La balena puo` vivere sotto l'acqua per un lungo tempo.
The whale can live under water for a long time.
v2) Le piante non possono vivere senza la luce.
Plants cannot live without light.
v3) Ho vissuto molto bene quando ero in California.
I had a good life when I was in California.
v4) Dopo la malattia e` vissuto ancora a lungo.
After the illness he still lived for a long time.