已知集合 $M=\left\{x \left\lvert\, x=2 m+\frac{1}{3}\right., m \in Z\right\}, N=\left\{x \left\lvert\, x=n-\frac{2}{3}\right., n \in Z\right\}$, $P=\left\{x \left\lvert\, x=p+\frac{1}{3}\right., p \in Z\right\}$, 则 $M, N, P$ 的关系（）
$\text{A.}$ $M=N \subsetneq P$
$\text{B.}$ $M \subsetneq N=P$
$\text{C.}$ $M \subsetneq N \subsetneq P$
$\text{D.}$ $N \subsetneq P \subsetneq M$