There is a nice thread over at Singing in the Reign by Michael Barber on the parallels between the prophetic succession from Elijah to Elisha and from John the Baptist to Christ.
With respect to the Elijah/Elisha and John/Jesus "succession" of prophethood - it is worth noting that in both cases the former "transferred his mission" to the latter at the Jordan River.
Elijah handed over the baton to Elisha at the Jordan. John handed over the baton to Christ at the Jordan.
In a certain sense, Moses also handed over power to Joshua before the Joshua crossed the Jordan. The Jordan River is a sign of the Kingdom of God being established in the Promised Land. Crossing the Jordan or entering the Jordan (John's baptism!) is a sign of covenantal renewal between the people of God and God Himself.
Also related to this is the miracle of the Transfiguration where Christ is seen with Moses and Elijah. These two visitors personify the Law and the Prophets, but they also point to their true prophetic successor - not Joshua and Elisha, but Jesus the Son of God.
(The names "Yah Shua" and "Eli Sha" both refer to "the Lord of salvation" and "God my salvation". Christ's name, "Yashua" corresponds to the meaning of each.)