More simply, an inertial frame is one that is not accelerating.
Velocity is "relative"- always measured with respect to something that is taken to be stationary. Acceleration is not relative so asserting that a frame of reference is or is not accelerating can be done independently of other frames.
Of course, in general relativity it is shown that such tests of acceleration depend on effects that couldbe attributed to forces such as gravity so the idea of an inertial frame becomes blurred in general relativity.
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