The reaction schemes A+Binert and A+AA, controlled by enhanced diffusion, are investigated. The participating particles are assumed to perform Lévy walks with Lévy exponents 1<2. Both theoretical expressions and numerical results are presented. Reaction behaviors are observed which indicate mixing properties. When compared with reactions controlled by Brownian motion we obtain fast- er processes, new kinetic patterns, and, more importantly, lower, -dependent, critical dimensions for the mean-field behavior. The latter suggests erosion of the segregation phenomenon.