If the criteria are always in row 2 of the same column as the formula, define a name called Criteria using:
=EVALUATE("{""*"&SUBSTITUTE(INDIRECT("R2C",0),",","*"",""*")&"*""}")
and then enter:
=SUM(SUMIF($A:$A,Criteria,$B:$B))
in F3 using Ctrl+Shift+Enter to array enter it.
If the criteria are just in the cell above the formula cell, use this for the name definition:
=EVALUATE("{""*"&SUBSTITUTE(INDIRECT("R[-1]C",0),",","*"",""*")&"*""}")
instead.