  In this paper we consider $L_{\infty}$-algebras equipped with complete
descending filtrations. We prove that, under some mild conditions, an
$L_{\infty}$ quasi-isomorphism $U: L \to \tilde{L}$ induces a weak equivalence
between the Deligne-Getzler-Hinich (DGH) $\infty$-groupoids corresponding to
$L$ and $\tilde{L}$, respectively. This paper may be considered as a modest
addition to foundational paper arXiv:math/0404003 by Ezra Getzler.
