  Layered doped Mott insulators, such as the cuprates, show unusual temperature
dependence of the resistivity. Intriguingly, the resistivity perpendicular to
the CuO$_2$ planes, $\rho_c(T)$, shows both metallic ($d\rho_c/dT > 0$) and
semi-conducting ($d\rho_c/dT<0$) behavior. We shed light on this puzzle by
calculating $\rho_c$ for the two-dimensional Hubbard model within plaquette
cellular dynamical mean-field theory and strong-coupling continuous-time
quantum Monte Carlo as the impurity solver. The temperature, $T$, and doping,
$\delta$, dependencies of $\rho_c$ are controlled by the first-order transition
between pseudogap and correlated metal phases from which superconductivity can
emerge. On the large doping side of the transition $\rho_c(T)$ is metallic,
while on the low-doping side $\rho_c(T)$ changes from metallic to
semi-conducting behavior with decreasing $T$. As a function of doping, the jump
in $\rho_c$ across the first-order transition evolves into a sharp crossover at
higher temperatures. This crossover coincides with the pseudogap temperature
$T^*$ in the single-particle density of states, the spin susceptibility and
other observables. Such coincidence in crossovers is expected along the
continuation of the first-order transition into the super-critical regime,
called the Widom line. This implies that not only the dynamic and the
thermodynamic properties but also the DC transport in the normal state are
governed by the hidden first-order transition. $\rho_c(T)$ has a
high-temperature quasi-linear regime where it can exceed the Mott-Ioffe-Regel
limit and when it has a minimum it is nearly parallel to the Widom line.
