White dwarfs (WDs) can increase their mass by accretion from companion stars, provided the mass-accretion rate is high enough to avoid nova eruptions. The accretion regimes that allow growth of the WDs are usually calculated assuming constant mass-transfer rates. However, it is possible that these systems are influenced by effects that cause the rate to fluctuate on various timescales. We investigate how long-term mass-transfer variability affects accreting WDs systems. We show that, if such variability is present, it expands the parameter space of binaries where the WD can effectively increase its mass. Furthermore, we find that the supernova type Ia (SNIa) rate is enhanced by a factor 2-2.5 to a rate that is comparable with the lower limit of the observed rates. The changes in the delay-time distribution allow for more SNIae in stellar populations with ages of a few Gyr. Thus, mass-transfer variability gives rise to a new formation channel of SNIa events that can significantly contribute to the SNIa rate. Mass-transfer variability is also likely to affect other binary populations through enhanced WD growth. For example, it may explain why WDs in cataclysmic variables are observed to be more massive than single WDs, on average.
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