What transition would you most likely use when supporting a claim with evidence? for instance however this means in other words

The best transition to use here would be For Instance. In using for instance, you could give an example or the evidence of the claim your have made in the prior sentence. 

Example.

Despite the huge #metoo movement, sexual harassment still happen to women everyday. For instance, walking around New York alone will sure end up with the women being catcalled.

Because anne thinks margot is jealous towards her and peters relationship.