  We study in this paper three different theories of gravitation with massive
gravitons - the modified Fierz-Pauli (FP) model, Massive Gravity and the
bimetric theory proposed by Visser - in linear perturbation theory around a
Minkowski and a flat FRW background. For the TT tensor perturbations we show
that the three theories give rise to the same dynamical equations and to the
same form of the Boltzmann equations for the radiative transfer in General
Relativity (GR). We then analyze vector perturbations in these theories and
show that they do not give the same results as in the previous case. We first
show that vector perturbations in Massive Gravity present the same form as
found in General Relativity, whereas in the modified FP theory the vector
gravitational-wave (GW) polarization modes ($\Psi_{3}$ amplitudes in the
Newman-Penrose (NP) formalism) do not decay too fast as it happens in the
former case. Rather, we show that such $\Psi_{3}$ polarization modes give rise
to an unusual vector Sachs-Wolfe effect, leaving a signature in the quadrupole
form $Y_{2,\pm 1}(\theta,\varphi)$ on the CMB polarization. We then derive the
details for the Thomson scattering of CMB photons for these $\Psi_{3}$ modes,
and then construct the correspondent Boltzmann equations. Based upon these
results we then qualitatively show that $\Psi_{3}$-mode vector signatures - if
they do exist - could clearly be distinguished on the CMB polarization from the
usual $\Psi_4$ tensor modes.
