It may be helpful to simplify accidentals when analyzing an interval.
If both notes have the same kind of accidentals...
the quality of the interval is the same as the quality of the interval without accidentals:
In the previous example all seconds are major. It's easier to analyze the first one without accidentals.
If one of the notes has a double sharp and the other has a sharp...
make the sharp note natural and the double sharp note sharp. The interval quality will remain the same:
In the previous example both fifths are augmented.
If one of the notes has a double flat and the other has a flat...
make the flat note natural and the double flat note flat. The interval quality will remain the same:
Both fourths in the previous example are augmented.