Neural networks that regress the displacement and associated covariance of an inertialmeasurement unit (IMU) purely from its accelerometer and gyroscope measurements havebecome key enablers to low-drift inertial odometry, but still ignore the physical roto-reflective symmetries inherent in IMU data, thus hindering generalization. In this work, weshow that IMU data, displacements and covariances transform equivariantly, when rotatedaround and reflected across planes parallel to gravity. We design a neural network thatequivariantly estimates a gravity-aligned frame from IMU data, leveraging tailored linearand non-linear layers, and uses it to canonicalize the data. We train an off-the-shelf inertialodometry network on this data and map its outputs back into the original frame, thusobtaining equivariant covariances and displacements. To highlight its generality, we applythe framework to both filter-based and end-to-end approaches and show better performanceon the TLIO, Aria, RIDI and OxIOD datasets than existing methods.