C major
E flat augmented raises the Bb to B natural.
E flat consists of 3 flats, B flat, E flat and A flat. E flat to B flat would be a perfect 5th interval as B flat is in E flat major, but because your question was E flat to B, B is a semitone up from B flat, this would mean the interval becomes a semitone larger, and a semitone larger from a perfect interval is augmented. Therefore, the answer to your question is an augmented 5th. Hope this helps :)
You simply move the key down one half step
The third in a B-flat scale is D.
Transposed up a minor third, B flat major becomes D flat major.
A major 3rd would be C, so an augmented 3rd would be C sharp.
E-flat
Ab major
An augmented third is an interval of five semitones, spanning three note names. An example of an augmented third is C to E sharp, or C flat to E.
C major
D major
Christmas carols can generally be transposed into any key.
The interval between B-flat and G is equal to a major 6th. Thus, if a song has been transposed from B-flat major to G major, it will be a major 6th higher.
E flat augmented raises the Bb to B natural.
E flat consists of 3 flats, B flat, E flat and A flat. E flat to B flat would be a perfect 5th interval as B flat is in E flat major, but because your question was E flat to B, B is a semitone up from B flat, this would mean the interval becomes a semitone larger, and a semitone larger from a perfect interval is augmented. Therefore, the answer to your question is an augmented 5th. Hope this helps :)
E A major second is equivalent to a whole note, or two semitones, and two semitones down from G-flat (which is enharmonically equivalent to F-sharp) is E, although it might be written as F-flat depending on the key signature. F-flat, E to G-flat would be a diminished 3rd, not a major second..