How do wavelet levels depend on one another?
I may be a little confused by your question (intuitive dependency?) but I think these two sources will help you wrap your head around the relationship between levels in a DWT:


https://mil.ufl.edu/nechyba/www/eel6562/course_materials/t5.wavelets/intro_dwt.pdf
http://users.rowan.edu/~polikar/WTpart4.html


I think one way to think of it is because a DWT can be inverted, you can take a signal and perform a DWT on it and then you can reverse that DWT to get the original signal. So there's a clear dependance between levels in a DWT. I don't expect this answer to be accepted but i hope it can point you in the right direction to what you're looking for. 

Small quote from link #1

"In wavelet analysis, the Discrete Wavelet Transform (DWT) decomposes a signal into a set of mutually orthogonal wavelet basis functions. These functions diﬀer from sinusoidal basis functions in that they are spatially localized – that is, nonzero over only part of the total signal length. Furthermore, wavelet functions are dilated, translated and scaled versions of a a common function φ, known as the mother wavelet. As is the case in Fourier analysis, the DWT is invertible, so that the original signal can be completely recovered from its DWT representation.
"