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Black hole (BH) triples represent one of the astrophysical pathways for BHmergers in the Universe detectable by LIGO and VIRGO. We study the formation ofBH triples via binary-binary encounters in dense clusters, showing thatone-third of triples formed through this channel are in a non-hierarchical,unstable configuration. We build a database of $32,000$ $N$-body simulations toinvestigate the evolution of these BH triples. Varying the mutual orbitalinclination, the three BH masses and the inner and outer eccentricities, weshow that retrograde, nearly planar configurations lead to a significantshrinkage of the inner binary. We find an universal trend of triple systems,namely that they tend to evolve toward prograde configurations and that theorbital flip, driven by the torque exerted on the inner BH binary (BHB) by theouter BH, leads in general to tighter inner orbits that, in some cases, mergewithin a Hubble time. We find that the mergers' mass distribution maps theoriginal BH binary spectrum. A large fraction of merging BHBs with initialseparation $1$ AU enter the $10^{-3}-10^{-1}$ Hz frequency band with largeeccentricities, thus representing potential eccentric LISA sources. Mergersoriginating from initially tighter BHB ($a\sim 0.01$ AU), instead, often haveeccentricities above 0.7 in the $1$ Hz band. This might imply that eccentricsources detected in high-frequency detectors are most likely connected with ahigh-velocity dispersion stellar environment, whereas eccentric sourcesdetected in low-frequency detectors are likely to develop in low-densityclusters. (Abridged)

Order in the chaos: eccentric black hole binary mergers in triples formed via strong binary-binary scatterings