A correlation of phase diagrams with sharp jumps of the magnetization, which were previously observed upon magnetic-field-induced AFM-FM transition, has been studied for a number of low-bandwidth manganites. This transition was shown to proceed in milliseconds and is connected to a spontaneous heat avalanche, but mechanisms responsible for an origin and a development of the avalanche are still unclear. Different manganites (Pr_0.67Ca_0.33MnO₃, Sm_0.55Sr_0.45Mn¹⁸O₃, Eu_0.58Sr_0.42MnO₃) are shown to characterize by a qualitatively identical phase diagram, with the slope of the AFM-FM boundary in the H-T-plane being negative, that is probably guides the avalanche-like character of the transition.