  We investigate how the voltage control of the exciton lateral dipole moment
induces a transition from singly to doubly connected topology in type II
InAs/GaAsSb quantum dots. The latter causes visible Aharonov-Bohm oscillations
and a change of the exciton g-factor which are modulated by the applied bias.
The results are explained in the frame of realistic $\mathbf{k}\cdot\mathbf{p}$
and effective Hamiltonian models and could open a venue for new spin quantum
memories beyond the InAs/GaAs realm.
