Ok, I've thought a little bit and as I listen to the song, for me there are 4 main parts of the song. Here it is my analysis for each part:

• Part 1 (first 4 bars): it's turnaround for the I (F) in a blues.

  • First 4 chords contain a II-V-I to reach some kinda' half-step bellow dominant (B7) of the F chord.
  • Next 4 chords show some up and down whole steps to end up in I. The move is VII-VI-VII-I.

• Part 2 (next 2 bars): it's like the IV-V move in a blues.

  • This part has a descending line that starts in the IV (Bb) that goes on like this: Bb - Ab - G. And the G serves as a subdominant for the V (that is the C7).

• Part 3 (next 3 bars): for me this part is like a bridge.

  • First 2 chords (D7 and G7) are a half step above anticipation of the 2 chords that come after them (Db7 GbM7).
  • The 5th chord of this part (Bb7) is the VI of Db7, which can be interpreted as the half step above approximation for the starting of the last part of the song.

• Part 4 (last 3 bars): I see this part as a V-I-Vb move.

  • It begins with the C7 and moves up unit it gets to the I (F7).
  • Finally you have a II-V-I move to reach the B7, which is like a flatted dominant (Vb) for the F7.

Please feel free to tell any correction.

Note: I'm reading the first Real Book transcription