If you can rent it out with good cash flow relative to your debt it's OK if the equity fluctuates.

How much have others seen the rates fluctuate, and am I doing the right thing by checking rates daily with the lenders before locking in?  

I'm looking for long term tenants, several have stayed over 30 years, so the fluctuations of market value are irrelavent to me except when I'm selling.Bigger Pockets Podcast Guest #82

Or can it fluctuate?

Yes, this equity can go up or down in the short term as the market fluctuates, but that is really in the noise if you look at the long term trend ... if you are only concerned with the short term price movements, then you aught not be investing in buy-and-hold RE in the first place.

Also with the high fluctuation in AZ, cash flow is much harder to come by than appreciation in my opinion. 

However if you own the home free and clear, the cash flow awesome and you are insulated from risks of mortgage rate fluctuations.

However, there are a few other factors to consider when evaluating the risk of this investment:Market risk: Real estate markets can fluctuate, and it's important to consider the potential for changes in demand for rentals in your area.

Make provisions for these fluctuations in cash flow projections.

Make provisions for these fluctuations in cash flow projections.