  (Abridged) White dwarfs (WDs) undergoing unstable nuclear burning on their
surfaces, resulting in the nova phenomenon, have been considered as one of the
prospective candidates for the still elusive progenitors of SNeIa. We propose
that statistics of novae in nearby galaxies may be a powerful tool to gauge the
role of such systems in producing SNeIa. Using multicycle nova evolutionary
models, we compute the number and temporal distribution of novae that would be
produced by a typical (unstably burning) SNIa progenitor before reaching the
Chandrasekhar mass limit (M_ch) and exploding. Combined with the observed nova
rates, this can be used to constrain the maximal contribution of the nova
channel to the SNIa rate in nearby galaxies. The M31 nova rate measured by the
POINT-AGAPE survey is 65/yr. Assuming that all these novae will reach M_ch, we
obtain the maximal SNIa rate novae may produce to be (1-5)x10^-4/yr. This
constrains the overall contribution of the nova channel to the SNIa rate in M31
at <2-7%. Furthermore, ~80% of novae generated by a successful SNIa progenitor
have short decay times (t2<10 days), and are produced when the WD mass is close
to M_ch. We point out that statistics of such fast novae can provide a
sensitive diagnostic of the contribution of the nova channel to the final
stages of mass accumulation by the single degenerate (SD) SNIa progenitors. To
explore the prospects of their use, we investigate the efficiency of detecting
fast novae in an M31 nova survey of the PTF class. We find that a survey with
limiting magnitude of m_R~22 observing at least every 2nd night will catch ~90%
of fast novae expected in the SD scenario. Such surveys should be detecting
fast novae in M31 at a rate of the order of >10^3xf per yr, where f is the
fraction of SNeIa which accreted in the unstable nuclear burning regime while
accumulating the final ~0.1M_sun before the SNIa explosion.
