Claim:
Within each of these three groups the chords are interchangeable:
Group 1: C7b9, Eb7b9, F#7b9, A7b9, Edim, Gdim, Bbdim, C#dim
Group 2: Db7b9, E7b9, G7b9, Bb7b9, Fdim, G#dim, Bdim, Ddim
Group 3: D7b9, F7b9, Ab7b9, B7b9, F#dim, Adim, Cdim, Ebdim
Proof:
(Without restrictions only for group 1)
C7b9: C E G Bb Db
Eb7b9: Eb G Bb Db E
F#7b9: F# A# C# E G
A7b9: A C# E G A#
Edim: E G Bb Db
Gdim: G Bb Db E
Bbdim: Bb Db E G
C#dim: C# E G A#
The diminished chords are all made up of the same notes. The dominant seventh chords with the flat nine have common tones with the diminished chords, only the root differs. When replaced, the different root can be viewed as an altered tone that increases tension. With a dominant seventh chord, this tension is desired and is usually subsequently resolved by a major or minor chord.