I solved the problem by implementing the new UINavigationControllerDelegate Method animationControllerForOperation.
For example:
- (id<UIViewControllerAnimatedTransitioning>)navigationController:(UINavigationController     *)navigationController
                              animationControllerForOperation:(UINavigationControllerOperation)operation
                                           fromViewController:(UIViewController *)fromVC
                                             toViewController:(UIViewController *)toVC
{
PushTransition* transition = [PushTransition new];
[transition setNavigationControllerOperation: operation];
return transition;
}
PushTransition is a class that implements the UIViewControllerAnimatedTransitioning protocol and the two methods transitionDuration and animateTransition from that protocol. Additionally, i have added a property to pass the operation (tells me if it is a push or pop transition).
Just put the animation code for moving the views into the animateTransition as follows:
// the containerView is the superview during the animation process.
UIView *container = transitionContext.containerView;
UIViewController *fromVC = [transitionContext viewControllerForKey:UITransitionContextFromViewControllerKey];
UIViewController *toVC = [transitionContext viewControllerForKey:UITransitionContextToViewControllerKey];
UIView *fromView = fromVC.view;
UIView *toView = toVC.view;
CGFloat containerWidth = container.frame.size.width;
// Set the needed frames to animate.
CGRect toInitialFrame = [container frame];
CGRect fromDestinationFrame = fromView.frame;
if ([self navigationControllerOperation] == UINavigationControllerOperationPush)
{
    toInitialFrame.origin.x = containerWidth;
    toView.frame = toInitialFrame;
    fromDestinationFrame.origin.x = -containerWidth;
}
else if ([self navigationControllerOperation] == UINavigationControllerOperationPop)
{
    toInitialFrame.origin.x = -containerWidth;
    toView.frame = toInitialFrame;
    fromDestinationFrame.origin.x = containerWidth;
}
// Create a screenshot of the toView.
UIView *move = [toView snapshotViewAfterScreenUpdates:YES];
move.frame = toView.frame;
[container addSubview:move];
[UIView animateWithDuration:TRANSITION_DURATION delay:0
     usingSpringWithDamping:1000 initialSpringVelocity:1
                    options:0 animations:^{
                        move.frame = container.frame;
                        fromView.frame = fromDestinationFrame;
                    }
                 completion:^(BOOL finished) {
                     if (![[container subviews] containsObject:toView])
                     {
                         [container addSubview:toView];
                     }
                     toView.frame = container.frame;
                     [fromView removeFromSuperview];
                     [move removeFromSuperview];
                     [transitionContext completeTransition: YES];
                 }];
described it and you can you are done. Additionally you can make any push or pop animation you like.