  Several perturbation tools are established in the volume preserving setting
allowing for the pasting, extension, localized smoothing and local
linearization of vector fields. The pasting and local linearization hold in all
classes of regularity ranging from $C^{1}$ to $C^{\infty}$ (H\"older included).
For diffeomorphisms, a conservative linearized version of Franks lemma is
proved in the $C^{r,\alpha}$ ($r\in\mathbb{Z}^+$, $0<\alpha <1$) and
$C^{\infty}$ settings, the resulting diffeomorphism having the same regularity
as the original one.
