A possible indicator of potential Iranian leverage over the KRG (and especially the PUK):

SULEIMANIYYA: Iran's closure of its frontier with Iraq is costing the autonomous Kurdish region $1 million a day, a government minister said on Wednesday, as trucks remained stuck at the border.

...

Iran said on Monday it was closing its frontier with Iraq in protest at the detention last week of Iranian national Mahmudi Farhadi by US troops.
Full AFP story here. Reuters account here.