itunes and iphone app problem

wondering if anyone knows more details about how itunes keeps track of iphone apps (filenames, directories, etc etc...)...this is on a mac

I have an app that appears to be stuck it hangs on download and never finishes.

The problem is I clicked to delete it from itunes so it should no longer be there, clicking on apps does not show it, nor does the file show up in the actual directly itunes stores the apps. On the iphone doesn't show the app but if you go to the app store it shows that it is installed.

I've tried re-purchasing/downloading/syncing (it is a free app) and the iphone says sync to itunes, itunes says already purchased.

 

finally got it, copied an old .ipa file from time machine to the directory on the mac, synced the iphone, updated apps from the iphone (failed once, worked second time), then synced the iphone back to itunes and it appears that everything is good now