Liquid kit Nitrate(NO3) tests (most of them) also measure nitrite(NO2) to some extent, therefor they are more accurate at showing you nitrate(NO3) *after* the filter has cycled and you are getting readings of zero for nitrite(NO2.) What this means is that trying to interpret the nitrate readings during the second phase ("nitrite spike") of fishless can be confusing at the least. Even though the nitrite(NO2) appears spiked to you (because of the ceiling of the nitrite test), in actuality its bouncing around out at higher numbers and the nitrate(NO3) test will be bounced by this, thus the back and forth numbers.
OK, so what to do? Pay attention just to your ammonia, nitrite(NO2), pH and your timings, those are the important indicators of fishless cycling progress and conditions. In fishless cycling its always ideal to be able to "just leave it" as far as water changes go, but during the "nitrite spike" phase and beyond, its not necessarily a setback to do the occasional water change. What you do in this case is a large (90%, as of course small water changes have "no meaning" during fishless) gravel-clean-water-change and then recharge with ammonia (and baking soda if you happen to be having to use that.) Sometimes we refer to this as a "kickstart" for the people who have low KH/pH. What it also accomplishes is to make the nitrate(NO3) measurements more accurate for a while.
~~waterdrop~~