Evolution of the EKM timescale (given by Eq. (13)) for various configurations of three-body systems, as a function of the semi-major axis, for a companion eccentricity e_c = 0.1 (left), and outer binary eccentricity and semi-major axis, for an asteroid belt located at a_ast = 1 AU (right), for a low mass companion M_c = 1 M_⊙ corresponding to DNS, NSMS and NSWD systems (top), and a high mass companion M_c = 10 M_⊙ corresponding to NSMS and NSBH systems (bottom). The shadowed region on the left panels represents the forbidden configurations where the outer binary is closer than the inner binary. On the right panels, these forbidden configuration lies on the left-hand side of the vertical dashed line. The gray boxes on the right panels represent the parameters spaces where the different systems considered here are expected to lie. The solid lines show the limit where the timescale is shorter than one year (leading to transient events). On the left panels, the gray thin horizontal dashed lines and the arrows indicate the parameter-space in which the different systems would lie (Table 1).