Evolutionary stages of triples with a CHE inner binary that result in TMT with an inner BBH. Depending on the properties of the triple at the onset of TMT, mass transfer occurs via BA or the formation of a CBD. The masses of the three companions are indicated at the ZAMS (M_ZAMS), MS (M_MS), and helium MS (M_HeMS) phases. Furthermore, the BH mass (M_BH), pre-tertiary mass-transfer mass (M_{pre − TMT}), envelope mass (M_env), and core mass (M_core) are indicated. The grey and red crosses denote the centre of mass of the inner binary and outer binary, respectively. The figure is not to scale and has been adapted from van Son et al. (2022).