In its decomposition, hydrogen peroxide reacts to yeast because it is a catalyst that speeds up the reaction time. When hydrogen peroxide decomposes naturally into to water and oxygen, it does so slowly.
However, by adding active yeast to a solution of peroxide, the reaction time speeds up. In middle school, one chemistry experiment that illustrates this reaction is the addition of 3 percent hydrogen peroxide, active yeast and a small quantity of dish soap. What happens is that oxygen gas bubbles produce quickly and the soap begins to create foam. This shows that the active yeast is a catalyst.