Trying to do the following:
animTimeChange = AnimationUtils.loadAnimation(this, android.R.anim.slide_in_left);
itemTime.startAnimation(animTimeChange);
itemTime
TextSwitcher is exactly what you should be using for this. Check out the API Demo for TextSwitcher.
The way you should implement this is in your ListAdapter, provide TextSwitcher views to the ListView instead of TextViews. Then you can just call TextSwitcher.setText() on the list item you want to change.
Note that you should imediately get rid of your reference to the list item to avoid REALLY messing up listview.