Polystyrene-b-poly(acrylic acid) vesicles prepared in dioxane/water mixtures are equilibrium structures that respond to changes in the solvent composition by changing their size. An increase in vesicle size can be induced by adding water and occurs by vesicle fusion, while a decrease in vesicle size involves vesicle fission and can be induced by decreasing the water content in the solvent mixture. In this study, the kinetics of increase in vesicle size were examined. We evaluate the relaxation times of the process and determine the effect of factors such as the water content in the solvent mixture, the extent of perturbation in the solvent composition, the initial polymer concentration, and the acrylic acid block length on the rates. After adding water, the fusion of vesicles in solution was followed by measuring the change in turbidity as a function of time, and the relaxation times were extracted from the resulting turbidity vs time plots. The results show that the kinetics of increase in vesicle size become progressively slower as the water content increases, while increasing the magnitude of perturbation (i.e., the amount of water added) results in faster rates. Increasing the initial polymer concentration or the acrylic acid block length changes vesicle size and vesicle concentration and causes an increase in the rate of vesicle fusion.