This track for Cassidy is somewhat based on the version that appears on the Without A Net album. It is basically a study in “enharmonic modes”–modes that are made up of the same notes, but with different key centers.
It starts in E, and the chords in the piano and rhythm guitar indicate the lydian mode. After 16 bars (4 phrases of 4 measures each), the chords modulate to the mode of F# mixolydian. Note that this is the same notes as E lydian, but the tonal center moves up to F#. Then it goes back to E lydian for 4 measures, up to F# mixolydian again for 4, and then finally goes to G# aeolian–also the same notes as E lydian and F# mixolydian, now centered around the sound of G#m. Notice how, even though your palette of notes stays the same through all of this, the “vibe” makes a noticeable shift when the chord changes.
At this point, the bridge of the song would normally be played again, but for our purposes here, the loop just starts back over on E lydian.