  We study the instanton partition functions of two well-known superconformal
field theories with mass deformations. Two types of anomaly equations, namely,
the modular anomaly and holomorphic anomaly, have been discovered in the
literature. We provide a clean solution to the long standing puzzle about their
precise relation, and obtain some universal formulas. We show that the
partition function is invariant under the SL(2,Z) duality which exchanges
theories at strong coupling with those of weak coupling.
