[self.navigationController pushViewController:viewController animated:YES];

UIViewController *newVC = ...;
NSMutableArray *vcs =  [NSMutableArray arrayWithArray:self.navigationController.viewControllers];
[vcs insertObject:newVC atIndex:[vcs count]-1];
[self.navigationController setViewControllers:vcs animated:NO];
[self.navigationController popViewControllerAnimated:YES];

CATransition *transition = [CATransition animation];
transition.duration = 0.45;
transition.timingFunction = [CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionDefault];
transition.type = kCATransitionFromLeft;
[transition setType:kCATransitionPush];
transition.subtype = kCATransitionFromLeft;
transition.delegate = self;
[self.navigationController.view.layer addAnimation:transition forKey:nil];

self.navigationController.navigationBarHidden = NO;
[self.navigationController pushViewController:pageView animated:NO];

[UIView beginAnimations:@"rightToLeft" context:NULL];
CGRect newFrame = aView.frame;
newFrame.origin.x -= newFrame.size.width;
aView.frame = newFrame;
[UIView commitAnimations];

CATransition *transition = [CATransition animation];
transition.duration = 0.3f;
transition.timingFunction = [CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionEaseInEaseOut];
transition.type = kCATransitionReveal;
[self.navigationController.view.layer addAnimation:transition forKey:nil];
[self.navigationController pushViewController:phoneServicesViewController animated:NO];

Try this :
//Push effect in reverse way
    CATransition* transition = [CATransition animation];
    transition.duration = 0.75;
    transition.type = kCATransitionPush;
    transition.subtype = kCATransitionFromLeft;
    [self.navigationController.view.layer addAnimation:transition forKey:kCATransition];
    [self.navigationController pushViewController:vc animated:NO];