  We consider real-valued solutions $u=u(x|s),x\in\mathbb{R}$ of the second
Painlev\'e equation $u_{xx}=xu+2u^3$ which are parametrized in terms of the
monodromy data $s\equiv(s_1,s_2,s_3)\subset\mathbb{C}^3$ of the associated
Flaschka-Newell system of rational differential equations. Our analysis
describes the transition, as $x\rightarrow-\infty$, between the oscillatory
power-like decay asymptotics for $|s_1|<1$ (Ablowitz-Segur) to the power-like
growth behavior for $|s_1|=1$ (Hastings-McLeod) and from the latter to the
singular oscillatory power-like growth for $|s_1|>1$ (Kapaev). It is shown that
the transition asymptotics are of Boutroux type, i.e. they are expressed in
terms of Jacobi elliptic functions. As applications of our results we obtain
asymptotics for the Airy kernel determinant $\det(I-\gamma
K_{\textnormal{Ai}})|_{L^2(x,\infty)}$ in a double scaling limit
$x\rightarrow-\infty,\gamma\uparrow 1$ as well as asymptotics for the spectrum
of $K_{\textnormal{Ai}}$.
