Testing of the newly built PisaMover has started and the official inauguration is expected for the end of the year.
The PisaMover will connect PSA airport to the Pisa Centrale train station.
It's a convenient feature for those who intend using PSA airport to head to the Cinque Terre or Tuscany, including Florence.
The construction of the new longer runway at Florence (FLR) airport is still awaiting approval of the Environmental Impact Analysis by the competent authorities, but is also undergoing court challenges brought up by local environmentalists' and NIMBY groups, so I don't expect they will start working on it anytime soon.
Both PSA and FLR airports are under the same airport management operator: Toscana Aeroporti S.p.A.