I don't think it's the same looking at the spellings of the major and minor pents. First of all, combining both scales doesn't include all the chromatic tones.
MAJOR PENT
1 2 3 5 6
c d e g a
MINOR PENT SPELLING
1 b3 4 5 b7
c eb f g Bb
BLUES SPELLING
1 b3 4 b5 5 b7
c eb f f# g Bb
I'm not very experienced in blues playing and I know they do something like mix up the major and minor pents including the 'blue note' of the b5.
My approach is just simply a visual approach where I visualise the Eb minor pent over the C major scale (or the minor pent 4 'clicks' away from the major root in the cycle of 5ths, e.g. Bb minor pent over G major). It works for me to easily come up with outside sounds which I don't think you'd recognize as blues. Mixing these up one can come up with quite 'Holdsworthian' sounds (for want of a better word).
If there is any relationship, it's that which you see from the cycle of fifths, i.e. relating the Eb to the C, however when you normally think of these two (me at least) I think of the C minor scale (and consequently the C minor pent) derived from Eb major, i.e. the Aeolian mode - not the other way round. Eb minor pent has no derivation from C major as far as I can see (music professors help me out here
) except that it's the 'inverse'.
Like I say - I'm sure this is called something somewhere, I just don't know what it is, so I call it 'inverse' for my personal reference.