Anhydrides reversibly react with water to form a respective acid or base. For example, $\ce{CO2}$ is the anhydride of $\ce{H2CO3}$:
$$\ce{CO2 + H2O <=> H2CO3}.\tag{R1}$$
Acidic anhydride can be obtained by removing water from acid. Nitroperoxynitrate appears to be the anhydride of peroxynitric acid:
$$\ce{N2O7 + H2O <=> 2 HNO4},\tag{R2}$$
but I couldn't confirm it with a reputable source. Also, can we produce the anhydride of any acid or base by removing water?
There's for example trifluoroperacetic acid, which forms trifluoroperacetic acid anhydride. "[H]ydrogen peroxide – urea can be used to give the peracid. This method involves no water, so it gives a completely anhydrous peracid."
That might make a starting point for a Derek Lowe article similar to that he wrote on peroxides. I'd get a bang out of reading it! And all that lovely fluorine, too...
Acyl peroxides, such as acetyl peroxide, can potentially serve as mixed anhydrides of the peroxy acid and the normal acid:
$\ce{R–C(O)–O–O–C(O)–R +H2O -> R–C(O)–O–OH + HO–C(O)–R}$
(e.g. acyl peroxide: $\ce{R}=\ce{CH3}$)
However, they are rarely reacted in this way because the normal acid is typically not desired. To prevent this, hydrogen peroxide solution is used. In that case the reaction is usually rendered as
$\ce{R–C(O)–O–O–C(O)–R +H2O2 -> 2 R–C(O)–O–OH}$
But the same net reaction would be obtained if the anhydride reacts first with water and then the normal acid is oxidized by the hydrogen peroxide. So from an experimental point of view, whether the acyl peroxide reacts with water or not is a matter of bookkeeping.
