  We thoroughly analyze at the bosonic level, in the framework of Free
Differential Algebras (FDA), the role of 2-form potentials setting in
particular evidence the precise geometric formulation of the anti-Higgs
mechanism giving mass to the tensors. We then construct the (super)-FDA
encoding the coupling of vector-tensor multiplets in D=4, N=2 supergravity, by
solving the Bianchi identities in superspace and thus retrieving the full
theory up to 3-fermions terms in the supersymmetry transformation laws, leaving
the explicit construction of the Lagrangian to future work. We further explore
the extension of the bosonic FDA in the presence of higher p-form potentials,
focussing our attention to the particular case p=3, which would occur in the
construction of D=5, N=2 supergravity where some of the scalars are properly
dualized.
