Mesmerize rhymes with:
glamorize, memorize, polymerize, samurai's, samurais, summarize, accessorize, authorize, burglarize, categorize, characterize, circularize, colorize, computerize, containerize, demilitarize, depressurize, familiarize, glamorize, memorize, militarize, miniaturize, mischaracterize, motorize, pasteurize, plagiarize, polarize, polymerize, popularize, pressurize, pulverize, reauthorize, rubberize, samurai's, samurais, satirize, summarize, temporize, terrorize, theorize, vaporize, winterize
Mesmerize sounds like:
machineries, magaziner's, manzanares, mckenrick, mcmorris, mcnamara's, michener's, missionaries, monsignors