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Let $U_{q}^{-}(\mathfrak g)$ be the negative half of a quantumBorcherds-Bozec algebra $U_{q}(\mathfrak g)$ and $V(\lambda)$ be theirreducible highest weight module with $\lambda \in P^{+}$. In this paper, weinvestigate the structures, properties and their close connections betweenthree important bases of $U_{q}^{-}(\mathfrak g)$ and $V(\lambda)$; crystalbases, canonical bases and perfect bases.  We first re-construct crystal basis theory with modified Kashiwara operators.While going through Kashiwara's grand-loop argument, we prove several importantlemmas, which play crucial roles in the later developments of the paper.  Next, based on the theory of canonical bases on quantum Bocherds-Bozecalgebras, we introduce the notion of primitive canonical bases and prove thatprimitive canonical bases coincide with lower global bases.  Finally, we develop the perfect basis theory for quantum Borcherds-Bozecalgebras and prove the existence of lower and upper perfect bases for$U_{q}^{-}(\mathfrak g)$ and $V(\lambda)$. Moreover, we also prove theuniqueness of lower and upper perfect crystals. In particular, all the lowerand upper perfect crystals are isomorphic to $B(\infty)$ or $B(\lambda)$.

Global bases, canonical bases and perfect bases for quantum Borcherds-Bozec algebras