  We present extensive optical and near-infrared photometric and spectroscopic
observations of the stripped-envelope (SE) supernova SN 2010as. Spectroscopic
peculiarities, such as initially weak helium features and low expansion
velocities with a nearly flat evolution, place this object in the small family
of events previously identified as transitional Type Ib/c supernovae (SNe).
There is ubiquitous evidence of hydrogen, albeit weak, in this family of SNe,
indicating that they are in fact a peculiar kind of Type IIb SNe that we name
"flat-velocity Type IIb". The flat velocity evolution---which occurs at
different levels between 6000 and 8000 km/s for different SNe---suggests the
presence of a dense shell in the ejecta. Despite the spectroscopic
similarities, these objects show surprisingly diverse luminosities. We discuss
the possible physical or geometrical unification picture for such diversity.
Using archival HST images we associate SN 2010as with a massive cluster and
derive a progenitor age of ~6 Myr, assuming a single star-formation burst,
which is compatible with a Wolf-Rayet progenitor. Our hydrodynamical modelling,
on the contrary, indicates the pre-explosion mass was relatively low, of ~4
M_sol. The seeming contradiction between an young age and low pre-SN mass may
be solved by a massive interacting binary progenitor.
