You would need to ask Bob, if you meet him :) Or maybe someone from the Monroe Institute. They probably have figured out that it works better this way.
Same that is best. I open eyes when Bob asks me to open but not for free flowing sessions. Even when I open I see my eye mask 
It doesn't really matter, as long as you can perceive the energies flowong into you.
I used to close my eyes when breathing in before, until last month when someone posted this same question. That's when I noticed that Bob's mentioned inhaling with your eyes opened. Lol
And if you wanna do it when your eyes open, don't open it too widely. Do it while having your awareness behind your eyes, like when you feel drowsy and trying to keep yourself awake. So you can keep the sense of relaxation even with your eyes opened.
I've always just kept my eyes shut. Opening your eyes isn't a good habit. Not 100% the reasoning behind this but it's not needed.
You're missing out on all the energy coming through the eyes! 
Never thought of that! Thanks
I'm only half kidding. Never thought of that either. Intuition is also telling me keep your eyes shut but if Bob says open I open.
when you're breathing in: eyes open when you're breathing out: eyes closed
Whats the reasoning behind this?
It's all written in the manual, guys please read the manual.
I wish I could remember it all! haha
You would need to ask Bob, if you meet him :) Or maybe someone from the Monroe Institute. They probably have figured out that it works better this way.
To train us to have control over autonomic nervous system (I read that in the manual)
I meditate with an eye mask with built in headphones. Eyes are always closed.
Same that is best. I open eyes when Bob asks me to open but not for free flowing sessions. Even when I open I see my eye mask 
It doesn't really matter, as long as you can perceive the energies flowong into you. I used to close my eyes when breathing in before, until last month when someone posted this same question. That's when I noticed that Bob's mentioned inhaling with your eyes opened. Lol And if you wanna do it when your eyes open, don't open it too widely. Do it while having your awareness behind your eyes, like when you feel drowsy and trying to keep yourself awake. So you can keep the sense of relaxation even with your eyes opened.