We have visualized macroscopic transient pores in mechanically stretched giant vesicles. They can be observed only if the vesicles are prepared in a viscous solution to slow down the leak-out of the internal liquid. We study here theoretically the full dynamics of growth (driven by surface tension) and closure (driven by line tension) of these large pores. We write two coupled equations of the time evolution of the radii r(t) of the hole and R(t) of the vesicle, which both act on the release of the membrane tension. We find four periods in the life of a transient pore: (I) exponential growth of the young pore; (II) stop of the growth at a maximum radius rm; (III) slow closure limited by the leak-out; (IV) fast closure below a critical radius, when leak-out becomes negligible. Ultimately the membrane is completely resealed.