  In this paper, we prove a phase transition in the connectivity of Finitary
Random interlacements $\mathcal{FI}^{u,T}$ in $\mathbb{Z}^d$, with respect to
the average stopping time. For each $u>0$, with probability one
$\mathcal{FI}^{u,T}$ has no infinite connected component for all sufficiently
small $T>0$, and a unique infinite connected component for all sufficiently
large $T<\infty$. This answers a question of Bowen in the special case of
$\mathbb{Z}^d$.
