Let $\mathcal{F}=(X,B,f,\sigma,\gamma)$ be a stitched fibration with normal form $\mathcal{F}_{u}=(Y,B_{u},f_{u},\sigma_{0},\gamma_{0})$. Let $\ell\in\mathscr{L}_{\bar{Z}_{\text{nor}}}$ be the unique sequence determined by $(V,u)\in\mathscr{U}_{Z_{\text{nor}}}$ defining $\mathcal{F}_{u}$. We call $\inv(\mathcal{F}):=(\bar{Z}_{\text{nor}},\ell)$ the invariants of $\mathcal{F}$. We say that the invariants of $\mathcal{F}$ vanish if for all $k\in\mathbb{N}$, $\ell_{k}\equiv 0$ when restricted to the reduced fibres of $\mathcal{F}_{u}$. We say that the invariants of $\mathcal{F}$ are fibrewise constant if all the $\ell_{k}$’s are fibrewise constant.