  Linearized gravity in the Very Special Relativity (VSR) framework is
considered. We prove that this theory allows for a non-zero graviton mass $m_g$
without breaking gauge invariance nor modifying the relativistic dispersion
relation. We find the analytic solution for the new equations of motion in our
gauge choice, verifying as expected the existence of only two physical degrees
of freedom. Finally, through the geodesic deviation equation, we confront some
results for classic gravitational waves (GW) with the VSR ones: we see that the
ratios between VSR effects and classical ones are proportional to $(m_g/E)^2$,
$E$ being the energy of a graviton in the GW. For GW detectable by the
interferometers LIGO and VIRGO this ratio is at most $10^{-20}$. However, for
GW in the lower frequency range of future detectors, like LISA, the ratio
increases significantly to $ 10^{-10}$, that combined with the anisotropic
nature of VSR phenomena may lead to observable effects.
