Interval Overlap Finder

Given two lists of intervals representing time periods, your task is to identify all overlapping intervals between the two lists. An interval is defined as a pair of integers [start, end] where start ≤ end. Note that within each list, intervals may overlap or even be unsorted.

Your solution should:

1. Merge overlapping intervals within each list first, so that each list contains non-overlapping intervals.
2. Determine the common time spans between the two merged lists that represent overlapping intervals.
3. Return these overlapping intervals as a list, merged and sorted if necessary.

For example, given the following inputs:

• List A: [[1, 5], [3, 7], [8, 12]]
• List B: [[4, 10]]

After merging, List A would be processed into [[1, 7], [8, 12]], and then the overlapping intervals with List B would be determined accordingly.

You can assume the interval boundaries are integers. Think about edge cases where one list might have no intervals or where intervals just touch at the endpoints.

Write a function or method in the programming language of your choice that takes two lists of intervals as input and returns the list of overlapping intervals.