Merging heaps in O(log N)?

Can you merge two heaps in O(log N)? Turns out if they are leftist heaps, you can!
But what is a leftist heap, and how is it different from binary heap?

Recall that binary heap is both complete and balanced. Hence it looks something like this:

               1
             /   \
            2     3
           / \   /
          5   6 7
             Fig 1

It's clear that it supports O(log N) operations.

In contrast, this is what leftist heap looks like:

               1
              / \
             3   2
            /   /
           5   7
          /
         6
             Fig 2

It's neither complete nor balanced. Yet, it supports O(log N) operations too!

How does it work?