我如何用async await/promises重写这个嵌套的回调地狱函数？

function nestedCallbacks(arg1, arg2, callback) {
    someAsyncFunction1(arg1, function(err, result1) {
        if (err) {
            return callback(err);
        }
        someAsyncFunction2(result1, function(err, result2) {
            if (err) {
                return callback(err);
            }
            someAsyncFunction3(result2, function(err, result3) {
                if (err) {
                    return callback(err);
                }
                callback(null, result3);
            });
        });
    });
}

async function rewriteWithAsyncAwait(arg1, arg2) {
    try {
        const result1 = await someAsyncFunction1(arg1);
        const result2 = await someAsyncFunction2(result1);
        const result3 = await someAsyncFunction3(result2);
        return result3;
    } catch (error) {
        throw error;
    }
}