  The mechanisms that bring galaxies to strongly reduce their star formation
activity (star-formation quenching) is still poorly understood. To better study
galaxy evolution, we propose a classification based on the maps of the ionised
hydrogen distribution, traced by kpc-resolved, equivalent width of H$\alpha$
maps, and the nuclear activity of the galaxies using information from the BPT
diagnostic diagrams. Using these tools, we group a sample of 238 galaxies from
the CALIFA survey in six quenching stages (QS): objects dominated by recent
star formation; systems that present a quiescent-nuclear-ring structure in
their centre; galaxies that are centrally-quiescent; galaxies with no clear
pattern in their ionisation gas distribution - mixed; systems that posses only
a few star-forming regions - nearly-retired, or galaxies that are completely
quiescent - fully-retired. Regarding their nuclear activity, we further divide
the galaxies into two groups - active systems that host a weak or strong AGN in
their centre, and non-active objects. Galaxies grouped into quenching stage
classes occupy specific locations on the star-formation-rate versus stellar
mass diagram. The "Blue cloud" is populated by the star-forming and the
quiescent-nuclear-ring galaxies, the "Green valley" is populated by
centrally-quiescent and mixed systems, "Red sequence" by the nearly- and
fully-retired objects. Generally, galaxies that host a weak or strong AGN show
properties, comparable to the non-active counterparts at the same quenching
stages, except for the AGN-hosting star-forming systems. The degree of the
star-formation quenching increases along the present emission-line pattern
sequence from star-forming to fully-retired. The proposed emission-line classes
reinforce the "inside-out" quenching scenario, which foresees that the
suppression of the star-formation begins from the central regions of the
galaxies.
