The Avon River flows through Christchurch, England (Dorset/Hampshire border) — not any city in New Zealand.
Christchurch, New Zealand has the Avon River / Ōtākaro — a spring-fed urban river central to the city's identity. The Māori name Ōtākaro means "place of a game" (referencing traditional activities). This river was severely impacted by the 2011 earthquake (lateral spreading, liquefaction, bed elevation changes) but remains a defining feature.
The Hampshire Avon (one of five English "Avon" rivers — from Welsh *afon*, "river") flows through Salisbury and Christchurch, Dorset, into Christchurch Harbour. It's a chalk stream—globally rare habitat—renowned for trout and salmon fishing.
Both cities are named Christchurch. Both have Avon rivers. The New Zealand city was named after the English one (by the Canterbury Association, 1848). The river names reflect both linguistic transfer and independent application of "Avon" (river) to local waterways.
Specify the country when referencing "Christchurch" and "Avon River" to avoid trans-hemispheric confusion.