Applying TQFT to count regular coverings of Seifert 3-manifolds

I give a formula for computing the number of regular $\mathrm{\Gamma }$-coverings of closed orientable Seifert 3-manifolds, for a given finite group $\mathrm{\Gamma }$. The number is computed using a 3d TQFT with finite gauge group, through a cut-and-glue process.