Let me line this bulls--- out please.
No offense to anyone, but most of you are wrong.
First Jon, you speak of the use of an E7 within the cycle not equating. Totally wrong, the cycle does not care about chord quality or key. The root is what matters.
You are confusing key concept with the cycle concept and trust me, the two twains shall never meet or should they.
Diatonic substitution on the other hand has swung the concept to the other side of the spectrum.
When using chords interchangeably, you really are not doing a lot other than changing some basic diatonic chord option and experienced players use it only as a platform to go deeper into a cadence or creat a pivot point for a more complex substitution.
For example, the I vi iii are not what I consider true subs, rather interchangeable chords,
Why the Ebm ? Well, it is a tritone sub for an Amin which interchanged with with the I. This opened up new possibilities for the harmonic structure.