Notice
"Giant Steps" is Trane's first song that especially utilizes his famous Coltrane Changes formula. The formula uses 3 key centers in a cycle of Major Thirds/minor Sixths (B, Eb, G).
It's easier to understand the form if you view the first and last eight measures as two different sections as A & B.
It's important to know the II-V-I chords in each key:
G: Am7 D7 GMaj7
B:C#m7 F#7 BMaj7
Eb: Fm7 Bb7 EbMaj7
So the Coltrane Changes formula from Bmaj7 is:
UP m3 (D7)
UP P4 (GMaj7)
UP m3 (Bb7)
UP P4 (EbMaj7)
He then uses a II-V-I a tritone (flat 4) away from EbMaj7:
Am7 D7
to modulate to the new key center of G.
The above formula is again used but from GMaj7
UP m3 (Bb7)
UP P4 (EbMaj7)
UP m3 (F#7)
UP P4 (BMaj7)
He is essentially using Dominant chords as "pivots" to resolve (UP P4) to key centers (B, Eb, G) around the cycle of M3's/m6th's (B, Eb, G).
The B section elaborates on II-V-I's located a tritone away each time, except for the last measure, which just uses a II-V to get back to the top of the tune.
Musical cycles are useful and simple ways of visualizing intervals and chords progressions. There are only 7 musical cycles.
Of course it's great to understand the music theory behind the changes, but it's most important to improvise actual melody and not just exercises. This one takes some serious shedding.
At www.acousticpower.com there is a powertab of "Giant Steps" with a full transcription of Trane's solos.
I suggest taking the TAB of "Giant Steps," and paste in the chord melody for the HEAD and practice over the changes slowly.
Check out the chord melody for Countdown which uses Coltrane Changes, but in similar fashion to the changes of Tune-Up.
HAVE FUN!