Given a Galois cover of curves f over a field of characteristic p, the lifting problem asks whether there exists a Galois cover over a complete mixed characteristic discrete valuation ring whose reduction is f. In this talk, I will discuss the case where the Galois groups are elementary abelian p-groups. I will present a combinatorial criterion for lifting an elementary abelian p-cover, dependent on the branch loci of its p-cyclic subcovers. Moreover, I will talk about how branch points of a lift coalesce on the special fiber. Finally, I will demonstrate the construction of lifts for several families of (Z/2Z)^3-covers of various conductor types, both with equidistant branch locus geometry and non-equidistant branch locus geometry.