Lemma 3

If $F$ and $F'$ are two $q$-good filtrations on $M$, there exists an integer $m$ such that $F'_n \subset F_{n-m}$ for every $n \in \mathbf{Z}$. In fact, there exists $n_2$ such that $F'_n \subset q^{n-n_2}M$ for every $n$, hence $F'_n \subset F_{n-(n_2-n_1)}$ for every $n$.