The following diagram shows such an overlapping region:
For each overlapping column, there are 6 cells shared by both constituent Sudokus. As a result, the remaining 3 cells in both puzzles must contain the same 3 digits. These cells have been colored in the diagram. Together, all these cells occupy a single nonet in both puzzles. When the blue cells in one of these nonets no longer allow digit X, we can eliminate all candidates for this digit from the blue cells in the twin. When one of the yellow cells contains digit Y, we can lock this digit in the yellow cells in the twin, eliminating it from the green and blue cells.
This technique resembles the way Law of Leftovers works. The overlapping columns have a common area with 6 cells and there are two leftover areas with 3 cells each.