7th chord progressions / Diatonic sequence

A few questions arose a few days ago, going over new material i got from my teacher to keep me busy during the easter holiday.
Since he’s getting ready to tour Japan, he’s not going to be able to answer my questions any time soon (at least not before the end of the holiday). So that leaves me with either mucking about with something i don’t quite understand yet, or ask for help in this great community.

I got “Tune up” from Miles Davis to practice the chords, notes and improvisation. So far so good.
I also learned that this song has a II V I (7th) chord progression.
In order to have some decent improvisation i need to understand to what diatonic sequence the chords on each stave? (is that correct?) belong to.
For example, the first “stave” has the chords E-7, A7, and Dmaj7. These belong to the D sequence.
So, i’d be improvising in D major for that sequence.
The second stave has the C sequence, so again, improvising will be done in C major.
The third one has C-7, F7, Bbmaj7 and Ebmaj7. B sequence.

Now here’s something i don’t yet know. When i look at the major scales, which has sharps and flats, they don’t show up in the last chord progression. The major scale of B has 5#'s, but here are 2b’s.

I’m missing out on something but i don’t know what. Why is it that there are 2b’s?
Is it because there is no correlation to the major scale? Is it because it sounds better that way?
is it because it’s a diatonic sequence and that has other rules?

Sorry for the long post, i hope my ramblings are a bit clear.

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I think your third line is in the key of B-flat major (which has 2 flats), not B major (which, as you said, has 5 sharps). I’m definitely not a foremost expert in theory, but when I go through and draw the notes out for those chords (Cm7, F7 and Bb maj7), the two-flat key signature does fit the notes in those chords.

Editing to add, that Bb major does also look to work with the subsequent Eb major chord, which would be IV in the diatonic sequence for Bb major.

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Definitely B flat not B natural.

You write Bb in your chord progression so you maybe just had an oversight moment.

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I was kicking myself all the way to work when i read the replies this morning.
How could i be this stupid?
Thank you @southpaw6 and @Richard_close2u for the help.

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