Analytic Torsion for Fibred Boundary Metrics and Conic Degeneration

We study the renormalized analytic torsion of complete manifolds with fibred boundary metrics, also referred to as φ-metrics. We establish invariance of the torsion under suitable deformations of the metric, and establish a gluing formula. As an application, we relate the analytic torsions for complete φ- and incomplete wedge-metrics. As a simple consequence we recover a result by Guillarmou and Sher about analytic torsion under conic degeneration.