  The star formation quenching depends on environment, but a full understanding
of what mechanisms drive it is still missing. Exploiting a sample of galaxies
with masses $M_\ast>10^{9.8}M_\odot$, drawn from the WIde-field Nearby
Galaxy-cluster Survey (WINGS) and its recent extension OMEGAWINGS, we
investigate the star formation rate (SFR) as a function of stellar mass (M$_*$)
in galaxy clusters at $0.04<z<0.07$. We use non-member galaxies at
0.02$<$z$<$0.09 as field control sample. Overall, we find agreement between the
SFR-M$_*$ relation in the two environments, but detect a population of cluster
galaxies with reduced SFRs which is rare in the field. These {\it transition}
galaxies are mainly found within the cluster virial radius ($R_{200}$) but they
impact on the SFR-M$_*$ relation only within 0.6R$_{200}$. The ratio of
transition to PSF galaxies strongly depends on environment, being larger than
0.6 within 0.3R$_{200}$ and rapidly decreasing with distance, while it is
almost flat with $M_*$. As galaxies move downward from the SFR-M$_*$ main
sequence, they become redder and present older luminosity and mass weighted
ages. These trends, together with the analysis of the star formation histories,
suggest that transition galaxies have had a reduced SFR for the past 2-5 Gyr.
Our results are consistent with the hypothesis that the interaction of galaxies
with the intracluster medium via strangulation causes a gradual shut down of
star formation, giving birth to an evolved population of galaxies in transition
from being star forming to becoming passive.
