  We give a complete description of the possible Hausdorff dimensions of
escaping sets for meromorphic functions with a finite number of singular
values. More precisely, for any given $d\in [0,2]$ we show that there exists
such a meromorphic function for which the Hausdorff dimension of the escaping
set is equal to $d$. The main ingredient is to glue together suitable
meromorphic functions by using quasiconformal mappings. Moreover, we show that
there are uncountably many quasiconformally equivalent meromorphic functions
for which the escaping sets have different Hausdorff dimensions.
