I put together this graph showing daily community covid cases and significant changes to alert levels. Red means a tightening and green a loosening.
So after the first infection, we went to Level 4. Cases peaked around 80 and then as they fell to 60 areas outside Auckland went to Level 2 and then to Level 2 as they were around 10.
Auckland cases stayed between 10 and 25 for a couple of weeks and the Government relaxed Auckland to Level 3. For the first week cases stayed around 20 but have been steadily increasing. Despite that, they did a further relaxation for Auckland this week.
It looks like going from L4 to L3 in Auckland did lead to an increase in cases and we will find out soon if the firtehr relaxing continues that trend.