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Detecting and coherently characterizing thousands of gravitational-wavesignals is a core data-analysis challenge for the Laser Interferometer SpaceAntenna (LISA). Transient artifacts, or "glitches", with disparate morphologiesare expected to be present in the data, potentially affecting the scientificreturn of the mission. We present the first joint reconstruction of short-livedastrophysical signals and noise artifacts. Our analysis is inspired by glitchesobserved by the LISA Pathfinder mission, including both acceleration and fastdisplacement transients. We perform full Bayesian inference using LISAtime-delay interferometric data and gravitational waveforms describing mergersof massive black holes. We focus on a representative binary with adetector-frame total mass of $6 \times 10^7 M_\odot$ at redshift $5$, yieldinga signal lasting $\sim 30~\mathrm{h}$ in the LISA sensitivity band. We exploretwo glitch models of different flexibility, namely a fixed parametric familyand a shapelet decomposition. In the most challenging scenario, we report acomplete loss of the gravitational-wave signal if the glitch is ignored; moremodest glitches induce biases on the black-hole parameters. On the other hand,a joint inference approach fully sanitizes the reconstruction of both theastrophysical and the glitch signal. We also inject a variety of glitchmorphologies in isolation, without a superimposed gravitational signal, andshow we can identify the correct transient model. Our analysis is an importantstepping stone toward a realistic treatment of LISA data in the context of thehighly sought-after "global fit".

Glitch systematics on the observation of massive black-hole binaries with LISA