Let $X$ and $Y$ be CW complexes. Let $sk_{\bullet}(X)$ and $sk_{\bullet}(Y)$ denote the canonical skeleta filtrations of $X$ and $Y$, respectively. Suppose that we have isomorphisms on homotopy groups $\pi_n(sk_{i}(X))\simeq\pi_n(sk_{i}(Y))$ for all $i\in\mathbb{N}$.
Is there a name for this scenario?
Additionally, this implies that $X$ and $Y$ have th same number of $0$-cells, so I am wondering if there is any additional structure here.