I played blues harp for several years before my saxophonic adventures.
Bending notes on the harp is a case of chewing the notes in the mouth.
It's easier to do in the beginning with the inhale - suck - notes but with time and using the same techniques the blow notes will bend as well.
This is my take after doin' an awful lot've blowin' air down curly tubes.
I form my notes in the oral cavity, there's a lot goes on before the airstream even sets the reed in motion.
As far as I'm concerned it's the mouthbox where each note is created.
Just as I can chew, bite and chomp and manipulate food I also do the same to manage the air when I speak to produce dialects and manipulations of the sounds created by my vocal chords.
The same goes for creating and bending the notes on the saxophone.
It's not mouthpieces and reeds, it's controlling mouthboxes and tongues and lungs.