Context : We present the analysis of H \alpha 3 , an H \alpha narrow-band imaging follow-up survey of galaxies selected from the HI Arecibo Legacy Fast ALFA Survey ( ALFALFA ) in the Coma supercluster . Aims : Taking advantage of H \alpha 3 , which provides the complete census of the recent star formation in HI-rich galaxies in the local universe , we explored the hypothesis that a morphological sequence of galaxies of progressively earlier type and lower gas-content exists in the neighborhood of a rich cluster of galaxies such as Coma , with a specific star formation activity that decreases with increasing local galaxy density and velocity dispersion . Methods : By using the H \alpha hydrogen recombination line as a tracer of the ” instantaneous ” star formation , complemented with optical colors from SDSS , we investigated the relationships between atomic neutral gas and newly formed stars in different local galaxy density intervals , for many morphological types , and over a wide range of stellar masses ( 10 ^ { 9 } to 10 ^ { 11.5 } M _ { \odot } ) . Results : In the dwarf regime ( 8.5 < \log ( M _ { * } / M _ { \odot } ) < 9.5 ) we identify a four-step sequence of galaxies with progressively redder colors ( corrected for dust extinction ) , i.e. , of decreasing specific star formation , from ( 1 ) HI-rich late-type galaxies ( LTGs ) belonging to the blue cloud that exhibit extended plus nuclear star formation , ( 2 ) \sim 0.1 mag redder , HI-poor LTGs with nuclear star formation only , ( 3 ) \sim 0.35 mag redder , HI-poor galaxies without either extended or nuclear star formation , but with nuclear post-star-burst ( PSB ) signature , ( 4 ) \sim 0.5 mag redder early-type galaxies ( ETGs ) that belong to the red sequence , and show no gas or star formation on all scales . Along this sequence the quenching of the star formation proceeds radially outside-in . The progression toward redder colors found along this ” morphological ” ( gas content ) sequence is comparable to the one obtained from increasing the local galaxy density , from cosmic filaments ( 1 2 ) , to the rich clusters ( 2 3 4 ) . Conclusions : In the dwarf regime we find evidence for an evolution of HI-rich LTGs into ETGs through HI-poor LTGs and PSB galaxies driven by the environment . We identify ram-pressure as the mechanism most likely responsible for this transformation . We conclude that infall of galaxies has proceeded for the last 7.5 Gyr , building up the Coma cluster at a rate of approximately 100 galaxies with \log ( M _ { * } / M _ { \odot } ) > 9.0 per Gyr .