The Breakthrough in a Bishop Endgame

This morning I saw following interesting endgame position in a book

Of course, this is a better position for White. His dominate king position gives him a clear advantage. But will it be enough for a win?

                       1. White goes forward with his king side pawns

                                    2. The Bishop Improvement

                                     3. The Breakthrough

                                                       ***

Merry Christmas to all!

If you want read an extraordinary true story during the Christmas Days: http://en.e-stories.org/read-stories.php?&sto=6897