Is it possible to show pushViewController animation look like presentModalViewController but that has background functionality of pushViewCon
Try this :
UIViewController *yourViewController = [[UIViewController alloc]init];
[UIView beginAnimations: @"Showinfo"context: nil];
[UIView setAnimationCurve: UIViewAnimationCurveEaseInOut];
[UIView setAnimationDuration:0.75];
[self.navigationController pushViewController: yourViewController animated:NO];
[UIView setAnimationTransition:UIViewAnimationTransitionFlipFromRight forView:self.navigationController.view cache:NO];
[UIView commitAnimations];