Merger history of the hosts of LISA MBHBs. Left panel: cumulative distribution of the baryonic mass ratio () of the two galaxies involved in the interaction that brought the secondary MBH to the primary galaxy. Different columns correspond to different redshift bins: z = 1 ± 0.25 (left), z = 2 ± 0.25 (middle), and z = 3 ± 0.25 (right). The horizontal dashed grey lines highlight the values 0.1, 0.5, and 0.9. The shaded region corresponds to the merger ratios associated with major mergers in L-Galaxies. Right panel: same as left panel but for the values of the delay time, Δt_Bin, between the galaxy–galaxy merger and that of the binary. In this case, the shaded area represents the region where the merger signatures have vanished at the time of LISA detection. Dashed and dotted lines represent the same but for galaxy interactions with m_R > 0.2 and 0.01, respectively. In all panels, vertical dashed lines correspond to the Hubble time at z = 1 (left panel), z = 2 (middle panel), and z = 3 (right panel). In general, the distributions shown in these figures show that more than 50% of the LISA MBHBs result from galaxy mergers with a baryonic mass ratio of greater than 0.01, with a minor contribution to major mergers. We stress that these baryonic ratios do not imply that the binaries display the same mass ratios at inspiral and coalescence. This is due to the gas accretion of MBHBs along the galaxy evolution.