How did the reionization epoch make the universe "transparent"? I've been reading about the reionization epoch of the universe, and it isn't entirely clear to me.  

As I understand it, very shortly after the big bang the universe was ionized, with the electrons stripped from the protons of hydrogen. The way that it's described is that the universe was "opaque" (since it was filled with ionized gas). Then the universe cooled enough for neutral hydrogen to form again, and the universe became "transparent". When the first stars and galaxies began to form they reionized the universe.  

What I don't understand is that in illustrations of this reionization, during the reionization epoch, it seems that the universe isn't transparent, but filled with unionized IGM (neutral hydrogen). Then the ionizing radiation from the newly formed stars ionizes the medium and ... these bubbles of ionized regions grow and merge until the entire universe is ionized again (and is therefore transparent).   

Have I misunderstood when the universe is transparent? Or the definition of transparent? Would it be accurate to say that the present day universe is completely ionized? (Does this just mean that most matter is in the form of stars which can be considered ionized? Since it doesn't really seem immediately evident in everyday life that "everything is ionized")
Nowadays, the universe is mostly ionized, and transparent.

Transparent means that photons are able to travel long distances.

So there comes the confusion: How could it be that recombination made the Universe transparent, and reionization keep it transparent?

After the Big Bang we had a very small Universe, filled with ionized matter. That amount of ionized matter caused the photons to be short-lived, and thus the Universe were opaque.

Then it came the recombination, and most baryonic matter became neutral, the photons were able to travel long distances, and the Universe thus became transparent.

And it was expanding. And at the same time clusters of matter were collapsing.

The combination of these two factors made the intergalactic medium density to fall a lot. Not only were there much more space for the same matter, but also the matter was concentrated in small bunchs making almost all the space almost empty.


  The second phase change occurred once objects started to condense in the early universe that were energetic enough to ionize neutral hydrogen. As these objects formed and radiated energy, the universe reverted from being neutral, to once again being an ionized plasma. This occurred between 150 million and one billion years after the Big Bang (at a redshift 6 &lt; z &lt; 20). At that time, however, matter had been diffused by the expansion of the universe, and the scattering interactions of photons and electrons were much less frequent than before electron-proton recombination. Thus a universe full of low density ionized hydrogen will remain transparent, as is the case today. [1]


So when the clusters of matter collapsed enough to become galaxies with stars and these stars reionized the intergallactic medium, there were almost no matter there, so photons continued being free to travel without obstacles, and so the Universe remained transparent.

So, it has been transparent for two different reasons: neutrality of matter, after the recombination, and scarcity of matter, after the reionization.

1: http://en.wikipedia.org/wiki/Reionization#Background