why does a 12m eurodollar fly move with teh swap spread

assuming no moves in credit, have a look at:
-(ED?1 - 2* ED?5 + ED?9) to 2*ED?5-TUA

just trying to get my head around this, latter part is the swap spread - can someone please explain to me why these two are moving together, what exactly is the 12m fly representing?
 

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sorry but i'm not really following this... what about the ed?5 turning it into a fly... just confused how u take these different parts, which gets you the 12m fly, and its following the movement of swap vs. gov bond
 
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