Key center is so seamlessly fluid in this song. Let's just look at the chords and see what's happening.
The opening riff is in G, but the verse begins with this four-bar progression (each chord lasting two beats in four-four time):
A minor/Bb major/F major/C major/Bb major/F major/Bb major/G major
Here, we're obviously starting off with iii/IV/I in the key of F major, but it's a weak cadence and the chords keep moving. The C major chord sounds more like a point of rest than you'd think it might, and there's something to be said for thinking of this progression in terms of C mixolydian.
The G major chord at the end does signal a key center shift, but it happens as the chords keep coming at two beats each:
D major/E minor/F major/C major
After the preceding four-bar phrase, D major on the downbeat of bar five here definitely sounds like the tonic. The tonal center quickly moves away, however, with the F major chord in the next bar. As it turns out, the F and C chords here function as bVII and IV in G, as the verse then ends with the title words sung over these three chords:
A minor/F major/G major
G is definitely felt as the tonic here, with the F major chord meaning that we are now more certainly dealing with the mixolydian mode.
The bridge that follows moves back and forth between two chords only, E minor and F major. This curiously echoes the A minor to Bb major progression played at the beginning of the verse. Like that progression, it sounds like iii and IV chords (in what would here be the key of C major). The final F chord of the bridge works as a simple pivot, though, resuming its function as a bVII chord when the song slides back up to G major. The song is now in its home key once again and the opening riff is repeated.
In addition to the harmonic fluidity, there's is something to be said for the seamlessness of the metric irregularities in this song, too, and how both of these pleasingly relate to the song's subject matter.