  A new picture ``one-resonance - one-symmetry'' has been proposed recently to
reveal nature of the reparametrization symmetry in neutrino oscillation in
matter and where it resides: Symmetry of $i \leftrightarrow j$ state-exchange
type exists at around a resonance with $i$ and $j$ being the states which
participate in the level crossing. Consistently, the 1-2 and 1-3 state exchange
symmetries are identified at around the solar and atmospheric resonances,
respectively, in the locally-valid frameworks. On the other hand, the Denton
{\it et al.} (DMP) perturbation theory, a globally-valid framework, has the 1-2
exchange symmetry which is akin to the one in the aforementioned
solar-resonance perturbation (SRP) theory. In our picture, the symmetry must be
associated with the resonance, not the framework, and if so these two 1-2
symmetries must be identical to each other. We conduct a comparative study of
the 1-2 symmetries possessed by SRP and DMP to confirm their identity. An
almost identity is verified, but in a highly nontrivial way.
