Comparison of the evolution of a triple system with and without a tertiary star. Panels (a) and (b) illustrate the evolution of the inner binary with and without the third star respectively. In the system with the tertiary star, mass transfer is induced by perturbations from the third star, allowing the system to eventually enter the LISA frequency bandwidth. When evolved without a tertiary star the binary components remain too far apart to interact. Such a system does not enter the LISA frequency bandwidth. The legends are similar to those in Fig. 2. In addition, the yellow filling represents a star in the Asymptotic giant branch phase.