Cyrille, I think that often the plain b13 chords printed in fake books are really augmented chords; the fake book editor wants to suggest an inner line. For example, using Bb7, the editor wants to suggest an inner line (or reflect the melody line) of G, Gb, and F. A well-known example is Jobim's "Wave"
https://www.youtube.com/watch?v=a6KDpB6skA4. In measures 7 and 8, the chord progression is F#13, F#+, B9, indicating a chord progression in which the high note of each chord is D#, D, and C#. To me, a true b13 chord is a polychord. A Bb7 chord with a b13 would be voiced (for a pianist playing with a bassist) with a D and Ab in the left hand an a Gb triad in the right hand, containing the #9 and b13 and would often be marked as Bb7alt.
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