  By applying the delicate \textit{a priori} estimates for the equations of
$(\Phi,\Gamma)$, which is introduced in the previous work, we obtain some
multi-scale regularity criteria of the swirl component $u^{\theta}$ for the 3D
axisymmetric Navier-Stokes equations. In particularly, the solution
$\mathbf{u}$ can be continued beyond the time $T$, provided that $u^{\theta}$
satiesfies $$ u^{\theta} \in
L^{p}_{T}L^{q_{v}}_{v}L^{q_{h},w}_{h},~~\frac{2}{p}+\frac{1}{q_{v}}+\frac{2}{q_{h}}\leq
1, ~2<q_{h}\leq\infty,~\frac{1}{q_{v}}+\frac{2}{q_{h}}<1. $$
