The ‘Amerigo Vespucci’ airport is connected with the city centre by VOLAINBUS, a service provided by BUSITALIA - SITA Nord. This is a really shuttle service (about 20 minutes) between the airport terminal and the centre of Florence: no intermediate stops are made except in the outskirts of the railway station.
BusItalia: "Vola in Bus"
Cap - Autolinee
Sky Bus Lines Caronna (stopos in Prato - Pistoia - Montecatini)