These words are frequently used interchangeably, but not by careful users of language. Happen means "to take place," "to come to pass": "A fatal accident just happened at that intersection." Happen, which originally indicated the taking place of something by hap or chance, should be used for events that are spontaneous or accidental. Occur has much the same meaning as happen but is more specific as to time or event: "His election occurred the month before." That which is scheduled (prearranged) may be said to take place; that which occurs or happens is more likely to be unplanned. Transpire is a formal word that means "to escape from secrecy" and should not be used as a synonym for happen, occur, or take place. Its literal meaning is "to be emitted as a vapor," "to be breathed out." From this meaning, transpire has come to suggest leaking out and becoming known. One can ask "Has anything transpired during my absence?" but only if he means "Has any secret leaked out?" or "Has anything come to light that was previously hidden or unknown?" Since the correct use of transpire is limited, why not always say happen, occur, take place, come to pass, befall, or present itself?
Dictionary of problem words and expressions. Harry Shaw. 1975.