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We study the renormalized analytic torsion of complete manifolds with fibred boundary metrics, also referred to as -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 - and incomplete wedge-metrics. As a simple consequence we recover a result by Sher and Guillarmou about analytic torsion under conic degeneration.
Lye et al. (Thu,) studied this question.