Avatar Press likes to use variant covers to promote its series, particularly short-run limited series like Moore’s; besides their artistic merit, several of these covers have more to say about the contents of the book than readers might think.
The Book of the Dead incentive covers take their name from the Hay Necronomicon: The Book of the Dead, but their primary artistic styling comes from the Egyptian Book of Coming Forth By Day, popularly known as the Book of the Dead.
Neonomicon #1
The overall Egyptian theme follows the Egyptian Book of the Dead styling. The inverted pentacle with descending tentacles is a recurring image, and is superimposed on the pharoah’s mask. The symbols below the skull are from the “Tablet of R’leyh” illustration in the Hay Necronomicon.
Neonomicon #2
This symbol combines many elements of Western as well as Egyptian symbolism and mysticism. The two-headed serpent is the mythical amphisbaena; the serpent is coiled around the skull in such a way as to mimic the Uraeus on the royal crown of Egypt; while the serpent eating its own tail is probably the Ouroboros, a symbol of eternity, reinforced by being folded into a Möbius strip-like character. The figure in the lower loop is a collection of symbols probably intended to represent balance (note the symbols for male and female below and to either side of the triangle). The sigil beneath the top loop is similar to those in the Simon Necronomicon, but I believe is original.
Neonomicon #3
The seated goddess is Bast, goddess of Cats (and thus a favorite of H. P. Lovecraft), and the hieroglyphs to the left of her spell out her name. The sigils are, again reminiscent of those in the Simon Necronomicon, but appear to be original.
Neonomicon #4
The central radiating sigil appears in several places in the Simon Necronomicon; the flanking sigils appear to be unique, those stylistically based on those in the Simon Necronomicon. The central, amorphous, tentacled figure is probably meant to represent a Great Old One.
Facts in the Case of Alan Moore's Providence 
One point that doesn’t seem to have been mentioned for the cover of Neonomicon 2: while the central serpent is indeed arranged as a classic Ouroboros, it is also a depiction of Yig, the father of serpents.
Evidence for this is the text that runs vertically on both sides. The cryptic letters are actually a font called “Lovecraft’s Diary”, and can be found online. The text reads from top to bottom: “Yig the magnificient”, ending with a miniature serpent symbol, not found in the font itself, most likely decorative.
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