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System identification is a fundamental problem in reinforcement learning, control theory and signal processing, and the non-asymptotic analysis of the corresponding sample complexity is challenging and elusive, even for linear time-varying (LTV) systems. To tackle this challenge, we develop an episodic block model for the LTV system where the model parameters remain constant within each block but change from block to block. Based on the observation that the model parameters across different blocks are related, we treat each episodic block as a learning task and then run meta-learning over many blocks for system identification, using two steps, namely offline meta-learning and online adaptation. We carry out a comprehensive non-asymptotic analysis of the performance of meta-learning based system identification. To deal with the technical challenges rooted in the sample correlation and small sample sizes in each block, we devise a new two-scale martingale small-ball approach for offline meta-learning, for arbitrary model correlation structure across blocks. We then quantify the finite time error of online adaptation by leveraging recent advances in linear stochastic approximation with correlated samples.