Thinking your way to chess mastery - #2 Problem

I will post here Installment #2's problem.

It involves a game we went over,

GM Fier - GM Iturrizaga,  Sao Paolo 2009 Open

1. d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. Qc2 (Very popular) 

4...O-O!?  permitting white to grab the big center with 5. e4.

Fier did so, 5. e4 d6!? 6. Bd3 Nc6!? and very sharp play ensued.

Your puzzle is:  what did Iturrizaga plan on the alternate move 5. a3!?

Consider:

4....O-O!? 5. a3!? Bxc3 6. Qxc3  and now, as black, can you suggest some ways to get counterplay after 6....d6 -- now consider various white moves

7. bg5

7. b4

7. e3

7. Nf3

On each, give ways for black to get counterplay exploiting your temporary lead in development and castled king (versus white's not yet castled king).  You don't want to stay passive and slow here; that would just give white the bishop pair 'for free'.

Post your thoughts (explain the moves you give in English) as Comments at the Installment #2 solution blog placeholder.

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