Context. We present the analysis of Hα3, an Hα 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 Hα3, 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 Hα 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 ). Results. In the dwarf regime (8.5 < log (M * /M ) < 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) ∼0.1 mag redder, HI-poor LTGs with nuclear star formation only, (3) ∼0.35 mag redder, HI-poor galaxies without either extended or nuclear star formation, but with nuclear post-star-burst (PSB) signature, (4) ∼ 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 ) > 9.0 per Gyr.