Anadiplosis

anadiplosis \ˌa-nə-də-ˈplō-səs\ noun: repetition of the last word or phrase in one clause or sentence at the beginning of the next

Etymology: Late Latin, from Greek anadiplōsis repetition, from anadiploun to double, from ana- + diploun to double

Some prog geek quoted Genesis in Wikipedia’s article on anadiplosis: “The frog was a prince / The prince was a brick / The brick was an egg / The egg was a bird” (from the song Supper's Ready).