Perseus analysis of ἐπέσσυται:

ἐπισεύω (put in motion): pres ind mid 3rd sg

LSJ entry

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ἐπισεύω

ἐπισεύω, Ep. ἐπισσ- (as always in Hom.),

II. mostly Pass., hurry or hasten to or towards, ἐπεσσεύοντο δὲ λαοί Il. 2.86; ἔς τινα 13.757; ἐπεσσεύοντο νομόνδε to pasture, 18.575; νῆάδʼ (so Aristarch.) ἐπεσσεύοντο Od. 13.19; in hostile sense, rush upon or at, c. dat., νηυσὶν ἐπισσεύεσθαι Il. 15 347.

2. freq. in pf. part. Pass. ἐπεσσύμενος, with 3sg. plpf. ἐπέσσῠτο (used as an aor.): 3pl. aor. 1 ἐπέσσῠθεν Opp. C. 4.136 :—mostly in hostile sense, charge, ἐπέσσυτο δαίμονι ἶσος Il. 5.438, al.; ἰῷ ἐπεσσύμενον βάλε τείχεος ὑψηλοῖο struck him with an arrow from the wall as he rushed on, 12.388: c. dat., αὐτῷ μοι ἐπέσσυτο 5.459, cf. 21.227: c. acc., τεῖχος ἐπεσσύμενοι 12.143: c. gen., ἐπεσσύμενος πεδίοιο rushing, hurrying over the plain, 14.147, 22.26 (cf. διαπράσσω); also of fire, etc., ἠΰτε πῦρ, τό τʼ ἐπεσσύμενον πόλιν ἀνδρῶν . . φλεγέθει 17.737; κῦμα δεινὸν ἐπεσσύμενον Od. 5.314, cf. 431: also, without any hostile sense, to express rapid motion, c. dat., ὥς οἱ . . ὄνειρον ἐπέσσυτο 4.841: c. acc., ὡς πνοιὴ ἐπέσσυτο δέμνια swept over them, 6.20: c. inf., ἐπέσσυτο διώκειν he hasted on to follow, Il. 21.601, cf. A.R. 1.758: abs., χερσὶν ἐπεσσύμενος λάβε πέτρης Od. 5.428; ἐπεσσύμενος λάβε γούνων 22.310.