How far do you push this blind battle?

[Tosh]

Party Poker 15/30 Hold'em (10 handed)

Preflop: Hero is SB with A/images/graemlins/diamond.gif, K/images/graemlins/club.gif.
UTG folds, UTG+1 folds, UTG+2 folds, MP1 folds, MP2 folds, MP3 folds, CO folds, Button folds, <font color="CC3333">Hero raises</font>, <font color="CC3333">BB 3-bets</font>, <font color="CC3333">Hero caps</font>, BB calls.

Flop: (8 SB) 2/images/graemlins/spade.gif, 8/images/graemlins/spade.gif, 9/images/graemlins/heart.gif <font color="blue">(2 players) </font>
<font color="CC3333">Hero bets</font>, BB calls.

Turn: (5 BB) A/images/graemlins/heart.gif <font color="blue">(2 players) </font>
<font color="CC3333">Hero bets</font>, <font color="CC3333">BB raises</font>.

Keep raising, check raise the river, just call down or bet the river ?

[Nightwish]

Call and bet the river.

[elindauer]

Reraise. Your opponent will often hold a weaker ace and will call down. Also, your opponent is more likely than usual to be raising on a draw when this scare card hits the turn. Make him pay to draw.

I might go into check-call mode immediately after 3-betting, regardless of the future action, unless the river improved my hand.