Proposition 11.4. Let $A$ be a Noetherian local ring, $m$ its maximal ideal, $q$ an $m$-primary ideal, $M$ a finitely generated $A$-module, ($M_n$) a stable $q$-filtration of $M$. Then
i) $M/M_n$ is of finite length, for each $n\geqslant0$;
ii) for all sufficiently large $n$ this length is a polynomial $g(n)$ of degree $\leqslant s$ in $n$, where $s$ is the least number of generators of $q$
iii) the degree and leading coefficient of
$g(n)$ depend only on $M$ and $q$,
not on the chosen filtration.
Aren't the degree and leading coefficient of $g(n)$ independent of the choice of the primary ideal $q$ (meaning that we get the same degree and coefficient with another $m$-primary ideal $q'$)?