Title: Buoyancy glitches in pulsating stars revisited

Abstract: Sharp structural variations induce specific signatures on stellar pulsations that can be studied to infer localised information on the stratification of the star. This information is key to improve our understanding of the physical processes that lead to the structural variations and how to model them. Here we revisit and extend the analysis of the signature of different types of buoyancy glitches in gravity-mode and mixed-mode pulsators presented in earlier works, including glitches with step-like, Gaussian-like, and Dirac-$\delta$-like shapes. In particular, we provide analytical expressions for the perturbations to the periods and show that these can be reliably used in place of the expressions provided for the period spacings, with the advantage that the use of the new expressions does not require modes with consecutive radial orders to be observed. Based on a comparison with two limit cases and on simulated data, we further tested the accuracy of the expression for the Gaussian-like glitch signature whose derivation in an earlier work involved a significant approximation. We find that the least reliable glitch parameter inferred from fitting that expression is the amplitude, which can be up to a factor of two larger than the true amplitude, reaching this limit when the glitch is small. We further discuss the impact on the glitch signature of considering a glitch in the inner and outer half of the g-mode cavity, emphasising the break of symmetry that takes place in the case of mixed-mode pulsators.