  We show that a recent spectral flow approach proposed by
Berkolaiko-Cox-Marzuola for analyzing the nodal deficiency of the nodal
partition associated to an eigenfunction can be extended to more general
partitions. To be more precise, we work with spectral equipartitions that
satisfy a pair compatible condition. Nodal partitions and spectral minimal
partitions are examples of such partitions. Along the way, we discuss different
approaches to the Dirichlet-to-Neumann operators: via Aharonov-Bohm operators,
via a double covering argument, and via a slitting of the domain.
