In the article *Grothendieck Ring of pretriangulated categories* by Bondal-Larsen-Lunts, two dg-categories $\mathcal A$ and $\mathcal B$ are called *quasi-equivalent* if there is a chain of dg-categories and quasi-equivalences

$\mathcal A \leftarrow \mathcal C_1 \rightarrow \cdots \leftarrow \mathcal C_n \rightarrow \mathcal B$.

Another possibility, I think, would be to call $\mathcal A$ and $\mathcal B$ quasi-equivalent if they are isomorphic in the homotopy category $\mathrm{Ho}(\mathbf{dgcat})$. Clearly if $\mathcal A$ and $\mathcal B$ are quasi-equivalent as in the definition of Bondal-Larsen-Lunts, they are also isomorphic in $\mathrm{Ho}(\mathbf{dgcat})$. Is the converse true? What is the "better" definition of quasi-equivalent dg-categories?

Thanks in advance!