  This paper investigates on the possible systematic difference of Supernovae
Ia (SN Ia) properties related to the age and masses of the progenitors that
could introduce a systematic bias between low and high redshift SN Ia's. The
relation between the main features of the distribution of the delay times (DTD)
and the masses of the progenitors is illustrated for the single (SD) and double
degenerate (DD) models. Mixed models, which assume contributions from both the
SD and DD channels, are also presented and tested versus the observed
correlations between the SN Ia rates and the parent galaxy properties. It is
shown that these correlations can be accounted for with both single channel and
mixed models, and that the rate in S0 and E galaxies may effectively provide
clues on the contribution of SD progenitors to late epoch explosions. A wide
range of masses for the CO WD at the start of accretion is expected in almost
all galaxy types; only in galaxies of the earliest types the properties of the
progenitors are expected to be more uniform. For mixed models, late type
galaxies should host SD and DD explosions in comparable fractions, while in
early type galaxies DD explosions should largely prevail. Events hosted by star
forming galaxies span a wide range of delay times; \textit{prompt} events could
dominate only in the presence of a strong star-burst. It is concluded that
nearby SN Ia samples should well include the young, massive and hot progenitors
that necessarily dominate at high redshift.
