  We study the $p$-adic variation of triangulations over $p$-adic families of
$(\varphi,\Gamma)$-modules. In particular, we study certain canonical
sub-filtrations of the pointwise triangulations and show that they extend to
affinoid neighborhoods of crystalline points. This generalizes results of
Kedlaya, Pottharst and Xiao and (independently) Liu in the case where one
expects the entire triangulation to extend. As an application, we study the
ramification of weight parameters over natural $p$-adic families.
