According to equivalence principle, gravity can be treated like acceleration "locally". Based on this principle we can treat a non-inertial frame at rest and explain the fictitious forces (of Newton's Laws) as gravity. From this we can prove that time elapses at different rates at different positions in gravity and that the space is curved. But Einstein also said that the curved space-time can be treated "locally" as Minkowski space which is flat. Doesn't these two ideas contradict each other? From the former reason we are saying that space is curved locally because of gravity and latter is saying that it is flat. Could anyone please explain this reasoning.