Can you help me find a reference or explain how to find explicit Dehn twist generators for $MCG(D_n,\partial D_n)$, mapping class group of a $n$-punctured disc? (for the problem I am working on, $n=3,4$ would be sufficient).

PS: I know, for instance, there is an isomorphism between $MCG(D_n,\partial D_n)$ and the order $n$ braid group $B_n$, but I am not sure how the half twist generators of $MCG(D_n,\partial D_n)$ (which correspond to standard generators $\sigma_i$ of $B_n$ under the aforementioned isomorphism ) can be written in terms of Dehn twists.

Can you help me find a reference or explain how to find explicit Dehn twist generators for $MCG(S_{0,n})$, the mapping class group of a genus $0$ surface with $n$ boundary components, fixing the boundary components pointwise? (for the problem I am working on, $n=4,5$ would be sufficient.)

PS: My original post was about the mapping class group of a $n$-punctured sphere, but then I realized what I am looking for is Dehn twist generators for the mapping class group of a sphere with $n$ boundary components, so I edited the problem accordingly.

Can you help me find a reference or explain how to find explicit Dehn twist generators for $MCG(D_n,\partial D_n)$, mapping class group of a $n$-punctured disc? (for the problem I am working on, $n=3,4$ would be sufficient).

PS: I know, for instance, there is an isomorphism between $MCG(D_n,\partial D_n)$ and the order $n$ braid group $B_n$, but I am not sure how the half twist generators of $MCG(D_n,\partial D_n)$ (which correspond to standard generators $\sigma_i$ under the aforementioned isomorphism ) can be written in terms of Dehn twists.

Can you help me find a reference or explain how to find explicit Dehn twist generators for $MCG(D_n,\partial D_n)$, mapping class group of a $n$-punctured disc? (for the problem I am working on, $n=3,4$ would be sufficient).

PS: I know, for instance, there is an isomorphism between $MCG(D_n,\partial D_n)$ and the order $n$ braid group $B_n$, but I am not sure how the half twist generators of $MCG(D_n,\partial D_n)$ (which correspond to standard generators $\sigma_i$ of $B_n$ under the aforementioned isomorphism ) can be written in terms of Dehn twists.