Recent experiment [Sigrist et al., Phys. Rev. Lett. {\bf 98}, 036805 (2007)]
reported switches between 0 and π in the phase of Aharonov-Bohm
oscillations of the two-terminal differential conductance through a two-dot
ring with increasing voltage bias. Using a simple model, where one of the dots
contains multiple interacting levels, these findings are explained as a result
of transport through the interferometer being dominated at different biases by
quantum dot levels of different "parity" (i.e. the sign of the overlap integral
between the dot state and the states in the leads). The redistribution of
electron population between different levels with bias leads to the fact that
the number of switching events is not necessarily equal to the number of dot
levels, in agreement with experiment. For the same reason switching does not
always imply that the parity of levels is strictly alternating. Lastly, it is
demonstrated that the correlation between the first switching of the phase and
the onset of the inelastic cotunneling, as well as the sharp (rather than
gradual) change of phase when switching occurs, give reason to think that the
present interpretation of the experiment is preferable to the one based on
electrostatic AB effect.Comment: 12 pages, 9 figure