Greater Than Consecutive Sudoku (Daily Sudoku League #66)

Greater Than Consecutive Sudoku variation appeared Indian Sudoku Championship 2013 and I created this Sudoku puzzle to practice for this championship.

This Greater Than Consecutive Sudoku is my 66th contribution to The League of Extraordinary Ladies and Gentlemen. Can you solve this Sudoku puzzle?

Rules of Greater Than Consecutive Sudoku

Classic Sudoku Rules apply. Additionally, in all cases where the difference between two neighboring digits is 1, there is a greater or less sign between those digits. Digits must be placed in accordance with the signs.