Leading-edge vortices (LEV) dominate delta wing aerodynamics already at moderate angles of attack (α), inducing suction on the upper wing surface, thereby providing a nonlinear increase in lift. This results in smoother post-stall characteristics and enhanced maneuverability. In this regard, modern high-agility aircraft use multi-swept delta or strake-wing configurations to exploit multiple LEVs, enhancing their ability to perform complex maneuvers. However, at higher angles of attack, the stability of the LEVs diminishes, and vortex breakdown occurs, impairing the flight stability characteristics. This study investigates the formation, interaction, and breakdown of the LEVs around multi-swept hybrid-delta-wing configurations in the transonic flow regime, including shock-vortex interactions and their impact on vortex flow dynamics. Two main wing configurations are employed: a double-delta wing with leading-edge sweep angles of φ_2 = 75° for the strake and φ_3 = 52.5° for the main wing section, while the triple-delta wing incorporates a LEV controller segment with φ_1 = 52.5°. The relative leading-edge nose radii (r_n/c_r) of 0.00%, 0.25%, and 0.50% are analyzed for c_r = 0.802 m. Numerical simulations are performed using the TAU Code, developed by DLR. URANS computations employ the Spalart-Allmaras turbulence model in its negative formulation with rotation correction. Computations are performed at Ma = 0.75, 0.85, and 0.95 for 16° ≤ α ≤ 32° in 4° increments under β = 0° and 5°, with a time step of Δt = 2 × 10^-4 s. IDDES simulations are performed based on the URANS results, setting Δt to 2 · 10^-5 s, while α is varied with an increment of 8°. The numerical results are compared with wind tunnel measurements provided by DLR and Airbus Defence and Space.