How does transplanting different sets of Sharingan eyes work? I know the details of those eyes, I know their combination gives birth to the Eternal Mangekyo Sharingan. When Madara was almost blind Izuna gave him his eyes, the same thing happened with Itachi and Sasuke.

In these two cases we've seen the Eternal Mangekyo Sharingan and here comes my question:


In the first case, Madara was "blind" and Izuna had the good eyes, the combination was the Eternal. In the second case, Itachi was "blind" and Sasuke had the full eyes, giving birth to the Eternal. So it's indifferent which eye it's transplanted in the host body? (It doesn't matter that the good eye gets a disadvantaged blind eye?) 
As for the main question, how it is realized the "fusion" of 2 different eyes in one eye hole? I don't want to dig myself into the nerve/artery things. I'm interested more likely in the fact that how you mix 2 eyes into one and how the full eye and the blind eye, it's yet so much stronger??
After quite some searching I came to the sad conclusion there is barely any information available on how the 2 eyes get fused. Then again we can make some educated guesses thanks to some of the shown footage in the anime.

In episode 136 Itachi shows Sasuke how Madara got his Eternal Mangekyou Sharingan (EMS). Showing the following picture 



With this image we can deduce that the old eyes are not removed from the body, meaning there are 2 pairs of eyes in the body from that moment on. The most plausible reason to pass would be that the 2 eyes fuse in a similar way as to an artificial limb getting attached to a body. This would also explain the reason for blood ties as your body might reject people who are not directly blood linked.

This would also answer your first point, as the eyes fuse it does not matter whether the begin point was the blind eye or the still functioning eye as they will become one after all

How do the eyes exactly fuse? and how do they put 2 pairs of eyes in a body to begin with? Guess this is a sort of anime magic which is not really uncommon in Naruto to begin with (small sample (careful contains spoilers if not up to date with manga)