  It is known in vacuum that the three-flavor neutrino survival probability can
be approximated by the effective two-flavor form to first orders in $\epsilon
\equiv \Delta m^2_{21} / \Delta m^2_{31}$, with introduction of the effective
$\Delta m^2_{\alpha \alpha}$ ($\alpha = e, \mu, \tau$), in regions of neutrino
energy $E$ and baseline $L$ such that $\Delta m^2_{31} L / 2E \sim \pi$. Here,
we investigate the question of whether the similar effective two-flavor
approximation can be formulated for the survival probability in matter. Using a
perturbative framework with the expansion parameters $\epsilon$ and $s_{13}
\propto \sqrt{\epsilon}$, we give an affirmative answer to this question and
the resultant two-flavor form of the probability is valid to order $\epsilon$.
However, we observe a contrived feature of the effective $\Delta m^2_{\alpha
\alpha} (a)$ in matter. It ceases to be a combination of the fundamental
parameters and has energy dependence, which may be legitimate because it comes
from the matter potential. But, it turned out that $\Delta m^2_{\mu \mu} (a)$
becomes $L$-dependent, though $\Delta m^2_{ee} (a)$ is not, which casts doubt
on adequacy of the concept of effective $\Delta m^2$ in matter. We also find
that the appearance probability in vacuum admits, to order $\epsilon$, the
similar effective two-flavor form with a slightly different effective $\Delta
m^2_{\beta \alpha}$ from the disappearance channel. A general result is derived
to describe suppression of the matter effect in the oscillation probability.
