Seifert cobordisms and the Chen-Yang volume conjecture

We study the large $r$ asymptotic behavior of the Turaev-Viro invariants $T{V}_r(M;e^{\frac{2\pi i}{r}})$ of 3-manifolds with toroidal boundary, under the operation of gluing a Seifert-fibered 3-manifold along a component of $\mathrm{\partial }M$. We show that the Turaev-Viro invariants volume conjecture is closed under this operation. As an application we prove the volume conjecture for all Seifert fibered 3-manifolds with boundary and for large classes of graph 3-manifolds.