  We discuss physics of the three neutrino flavor transformation with
non-unitary mixing matrix, with particular attention to the correlation between
the $\nu$SM- and the $\alpha$ parameters which represent effect of unitarity
violating (UV) new physics. Toward the goal, a new perturbative framework is
created to illuminate the effect of non-unitarity in region of the solar-scale
enhanced oscillations. We refute the skepticism about the physical reality of
the $\nu$SM CP $\delta$ - $\alpha$ parameter phase correlation by analysis with
the SOL convention of $U_{\text{\tiny MNS}}$ in which $e^{ \pm i \delta}$ is
attached to $s_{12}$. Then, a comparative study between the solar- and
atmospheric-scale oscillation regions allowed by the framework reveals a
dynamical $\delta-$(blobs of the $\alpha$ parameters) correlation in the solar
oscillation region, in sharp contrast to the ``chiral'' type phase correlation
$[e^{- i \delta } \bar{\alpha}_{\mu e}, e^{ - i \delta} \bar{\alpha}_{\tau e},
\bar{\alpha}_{\tau \mu}]$ in the PDG convention seen in the atmospheric
oscillation region. An explicit perturbative calculation to first order in the
$\nu_{\mu} \rightarrow \nu_{e}$ channel allows us to decompose the UV related
part of the probability into the unitary evolution part and the genuine
non-unitary part. We observe that the effect of non-unitarity tends to cancel
between these two parts, as well as between the different $\alpha_{\beta
\gamma}$ parameters.
