On surgeries from lens space $L(p,1)$ to $L(q,2)$

We mainly use the d-invariant surgery formula established by Wu and Yang \cite{wu2025surgerieslensspacestype} to study the distance one surgeries along a homologically essential knot between lens spaces of the form $L(p,1)$ and $L(q,2)$ where $p,q$ are odd integers.