Grid of MT sequences for different MT efficiencies of α = 0.0 and β = [0.0, 0.25, 0.5, 0.75, 0.90, and 1.0], from the left to the right columns of the panels. Each row, as labeled at the right of the figure, corresponds to an initial value of M_BH,RLO = [5.0, 5.5, 6.0, 6.5, 7.0, 7.5, and 8.0] M_⊙. On the x-axis of each panel are shown the initial mass of the donor star M_2,RLO, the range of which is allowed to vary with β. The y-axis shows the initial orbital period P_RLO in days. Gray areas correspond to regions with initial M_BH,RLO, M_2,RLO, and P_RLO values that do not pass the analytic MT test or the initial ZAMS radius is greater than the Roche lobe. The white areas represent initial combinations of M_BH,RLO, M_2,RLO, and P_RLO that pass the analytic MT model, and for which we have made a detailed simulation with MESA. Circles indicate MT sequences that fail check 4, squares pass all checks and are persistent solutions according to Eq. (13). The colors indicate the relative likelihood of each detailed run.